Problem 52968. Easy Sequences 43: Least Common Fibonacci Number

Created by Ramon Villamangca

Solve Later

{"parts":[{"partUri":"/matlab/document.xml","contentType":"application/vnd.mathworks.matlab.code.document+xml","content":"<?xml version=\"1.0\" encoding=\"UTF-8\"?><w:document xmlns:w=\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\"><w:body><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>The Fibonacci sequence </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>F</w:t></w:r></w:customXml><w:r><w:t> is a series whose elements are numbers starting with </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>F_{1} =1</w:t></w:r></w:customXml><w:r><w:t> and </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>F_{2} =2</w:t></w:r></w:customXml><w:r><w:t>, and subsequent </w:t></w:r><w:hyperlink w:docLocation=\"https://en.wikipedia.org/wiki/Fibonacci_number\"><w:r><w:t>Fibonacci numbers</w:t></w:r></w:hyperlink><w:r><w:t> are defined recursively: </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>F_{n} =F_{n-1}+F_{n-2} </w:t></w:r></w:customXml><w:r><w:t>. The first 20 Fibonacci numbers are:</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t> </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"true\"/></w:customXmlPr><w:r><w:t>\\{1, \t2, \t3, \t5, \t8, \t13, \t21, \t34, \t55, \t89, \t144, \t233, \t377, \t610, \t987, \t1597, \t2584, \t4181, \t6765, 10946\\}</w:t></w:r></w:customXml></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:rPr><w:b/></w:rPr><w:t>Given two indices </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>n</w:t></w:r></w:customXml><w:r><w:rPr><w:b/></w:rPr><w:t> and </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>m</w:t></w:r></w:customXml><w:r><w:rPr><w:b/></w:rPr><w:t>, write a program to return the least common Fibonacci number, </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>LCF(n,m)</w:t></w:r></w:customXml><w:r><w:rPr><w:b/></w:rPr><w:t>, which is defined as the smallest Fibonacci number divisible by both </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>F_{n}</w:t></w:r></w:customXml><w:r><w:rPr><w:b/></w:rPr><w:t> and </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>F_{m}</w:t></w:r></w:customXml><w:r><w:rPr><w:b/></w:rPr><w:t>.</w:t></w:r><w:r><w:t> For example,</w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>LCF(3,4)=6765</w:t></w:r></w:customXml><w:r><w:t>, which is </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>F_{19}</w:t></w:r></w:customXml><w:r><w:t>, since </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>F_{3}=3</w:t></w:r></w:customXml><w:r><w:t> and </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>F_{4}=5</w:t></w:r></w:customXml><w:r><w:t> both divide </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>6765</w:t></w:r></w:customXml><w:r><w:t>.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>Since. the value of </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>LCF</w:t></w:r></w:customXml><w:r><w:t> may become large even if the values of </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>n</w:t></w:r></w:customXml><w:r><w:t> and </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>m</w:t></w:r></w:customXml><w:r><w:t> are relatively small, please output a vector containing the number of digits and the last </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>6</w:t></w:r></w:customXml><w:r><w:t> digits of </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>LCF</w:t></w:r></w:customXml><w:r><w:t>. Therefore, in the example above the output of </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>LCF(3,4)</w:t></w:r></w:customXml><w:r><w:t>, which has </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>4</w:t></w:r></w:customXml><w:r><w:t> digits, should be </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>[4\\ 6765]</w:t></w:r></w:customXml><w:r><w:t>.</w:t></w:r></w:p></w:body></w:document>","relationship":null}],"relationships":[{"relationshipType":"http://schemas.mathworks.com/matlab/code/2013/relationships/document","target":"/matlab/document.xml","relationshipId":"rId1"}]}

<div style = "text-align: start; line-height: 20.440000534057617px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: normal; text-decoration: none; white-space: normal; "><div style="block-size: 216px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; vertical-align: baseline; "><div style="block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; ">The Fibonacci sequence F<span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; "> is a series whose elements are numbers starting with <img src="data:image/png;base64,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" width="43.5" height="20" style="width: 43.5px; height: 20px;"><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; "> and <img src="data:image/png;base64,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" width="43.5" height="20" style="width: 43.5px; height: 20px;"><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; ">, and subsequent <a target='_blank' href = "https://en.wikipedia.org/wiki/Fibonacci_number">Fibonacci numbers</a><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; "> are defined recursively: <img src="data:image/png;base64,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" width="107" height="20" style="width: 107px; height: 20px;"><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; ">. The first 20 Fibonacci numbers are:</div><div style="block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; "> <img 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" width="519.5" height="19" style="width: 519.5px; height: 19px;"></div><div style="block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; ">Given two indices n<span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; "> and m<span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; ">, write a program to return the least common Fibonacci number, <img src="data:image/png;base64,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" width="69" height="19" style="width: 69px; height: 19px;"><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; ">, which is defined as the smallest Fibonacci number divisible by both <img src="data:image/png;base64,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" width="17" height="20" style="width: 17px; height: 20px;"><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; "> and <img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAACcAAAAoCAYAAAB99ePgAAAAAXNSR0IArs4c6QAAAERlWElmTU0AKgAAAAgAAYdpAAQAAAABAAAAGgAAAAAAA6ABAAMAAAABAAEAAKACAAQAAAABAAAAJ6ADAAQAAAABAAAAKAAAAAC8ZFV5AAACoklEQVRYCe2WSWgVQRCG474hQdyJ4DuIEBAPoiLEBXNxRVAvIrl7FhEUBT148OBBxJuHBBRyEMQElYDRg4KgIi64oBdFSIISERUUMS7fn1cFbeiXmXk6Qw5T8KV6/q7XVa863fMaGkorO1B2oOzAP3dgXMIKF5jfBklxsWUOIp6LTaTVJiYEtjE/Cy7D+iD2NuNr8Am0xkxYCi2wBGQDVZf/37Ok+G18wauYmKnQq6DY+bGALNr4lMHLgribjFVgzIYQ1eW38C4WkEVLU9x0FlwTLNoTjGPDX4j3YxN5aFtZ1LdUvpIiyYQUMYkhaTq3KVjlJeM3wbOGC2AQGvVg9tMHeXsV5J07PSKZvlwn3Buh/5fHpKukQhZdEW76J18NOq3NsBNa4RAUbvvI6F0bzfvdVmiBl4LibjFeBetAHTsOujqeQOGmLdcbwDt2IFLBC7RjET13SR3ywuTDi9iTf6ih+3xu/gQre3F9kSw6qYcjeiGSbnkvrr2QjCmTzCFOF6kXtyfl5woJ2xsUpneliq3X9FswfJ1NiSwU0yJhVekGzrv2rGZU7Ykmps6Afvd9Bl3cK+AhaEf85G9nrBP/HTZDou0gwguTH4Csv83UieWge1AneiU8haOgNbtBu/MAOkDaSRjVXjEbFuZjfdusHazYWr34R7AY1pp2BX8X9Bo8YlobvjBTMv9yGy2rrh5p32CRab2mZd0d+3h9rt2SdgQfv27aftO0/V/hsT0X4nRC+0GJ51nGaXh17DVMMm0DXp08Zc9/Od3yeZhO5kLogveWQIVMhfPwwzTfbnV0F8w2fdjlVZyuCNnFqhv+u8XGKtitxQZN+N3w0Sfy9HdYXFs4I0jynPEghA1Rx4agEybDmDIVP3dMVVQWU3ag7EAdHfgDdZGTuQ+F7fkAAAAASUVORK5CYII=" width="19.5" height="20" style="width: 19.5px; height: 20px;"><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; ">.<span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; "> For example,<img src="data:image/png;base64,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" width="114.5" height="19" style="width: 114.5px; height: 19px;"><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; ">, which is <img src="data:image/png;base64,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" width="22" height="20" style="width: 22px; height: 20px;"><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; ">, since <img src="data:image/png;base64,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" width="43.5" height="20" style="width: 43.5px; height: 20px;"><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; "> and <img src="data:image/png;base64,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" width="43.5" height="20" style="width: 43.5px; height: 20px;"><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; "> both divide <img src="data:image/png;base64,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" width="33" height="18" style="width: 33px; height: 18px;"><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; ">.</div><div style="block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; ">Since. the value of <img src="data:image/png;base64,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" width="33" height="18" style="width: 33px; height: 18px;"><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; "> may become large even if the values of n<span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; "> and m<span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; "> are relatively small, please output a vector containing the number of digits and the last 6<span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; "> digits of <img src="data:image/png;base64,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" width="33" height="18" style="width: 33px; height: 18px;"><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; ">. Therefore, in the example above the output of <img src="data:image/png;base64,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" width="65.5" height="19" style="width: 65.5px; height: 19px;"><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; ">, which has 4<span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; "> digits, should be <img src="data:image/png;base64,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" width="58" height="19" style="width: 58px; height: 19px;"><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; ">.</div></div></div>

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Last Solution submitted on Feb 19, 2023

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GeeTwo on 7 Dec 2022

That's not really a standard way to number F(n), (usually F(0):==0 and F(1):==1) but OK...

James on 2 Jun 2023 at 16:10

It's numbered like that because the lowest Fibonacci number divisible by F(a) and F(b) in the normal numbering system is F(lcm(a,b)). In the example here, you need to add one to everything to get that to work: lcm((3+1),(4+1)) = (19+1)

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Problem 52968. Easy Sequences 43: Least Common Fibonacci Number

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Problem 52968. Easy Sequences 43: Least Common Fibonacci Number

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