document.write( "Question 246694: What is the smallest positive integer divisible by all of the first ten positive integers? \n" ); document.write( "

Algebra.Com's Answer #180057 by jsmallt9(3758) $\"\"$ $\"About$

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Another way to word this problem is: \"Find the least common multiple (LCM) of the first ten positive integers.\"

\n" ); document.write( "One way to find LCM's is to use prime factorization:
\n" ); document.write( "1 = 1
\n" ); document.write( "2 = 2
\n" ); document.write( "3 = 3
\n" ); document.write( "4 = 2*2
\n" ); document.write( "5 = 5
\n" ); document.write( "6 = 2*3
\n" ); document.write( "7 = 7
\n" ); document.write( "8 = 2*2*2
\n" ); document.write( "9 = 3*3
\n" ); document.write( "10 = 2*5
\n" ); document.write( "The LCM of all of these will be the product of all the different factors. When a factor appears in more than one list of factors, use the longest string of this factor. So:
\n" ); document.write( "LCM = 1*2*2*2*3*3*5*7 = 2520
\n" ); document.write( "(The factors 2 and 3 appeared in more than one list of factors. So we use the longest string of each. We used the string of 3 2's from the list of factors for 8 and the string of 2 3's from the list of factors for 9.) \n" ); document.write( "

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