Continuing from our previous post, let’s\u00a0investigate one use of the prime\u00a0factorization:\u00a0 finding the least common multiple (LCM) of two\u00a0(or more) numbers.<\/p>\n
You can<\/em> find the LCM\u00a0just by listing the multiples of the numbers.\u00a0 For instance, imagine we need the LCM of 12 and 14:<\/p>\n 12, 24, 36, 48, 60, 72, 84<\/strong>, 96, 108….<\/p>\n 14, 28, 42, 56, 70, 84<\/strong>, ….<\/p>\n We see 84 is the first number to show up in both lists.\u00a0 Therefore, the LCM of 12 and 14 is 84.<\/p>\n Using the prime factorization method (once again, refer to the previous post for the quick details),<\/p>\n 12=2x2x3<\/p>\n 14=2×7<\/p>\n The LCM of 12 and 14 is the simplest combination that includes the prime factorizations of both:<\/p>\n 2x2x3x7<\/p>\n Note that 2x2x3x7 includes the prime factorization of 12 (which is 2x2x3, from above), and also includes the prime factorization of 14 (which is 2×7, also from above).\u00a0 2×7 does not occur written exactly that way, but since this is multiplication, we could change the order:<\/p>\n 2x3x2x7<\/p>\n Now 2×7 does occur just as written.\u00a0 Note that 2x2x3x7=2x3x2x7=84,\u00a0which was the LCM we got from the list method.<\/p>\n This simple trick to find the LCM is very handy as the numbers get bigger.<\/p>\n