There are three easy and simple ways to find the least common multiple of two numbers: the set intersection method, the prime factorization method, and the build-up method. The build-up method is a method to find the lowest common multiple or more commonly know as the LCM. In the build up method you express the numbers in their prime factor exponential form just like you do in the prime factorization method. This method to find the LCM or the least common multiple to me may be the hardest of the three. The example in the book says that for the numbers twenty-four and thirty-six you would express them as 24 = two to the power of three multiplied by three and you would express thirty-six as 36 = two to the power of two multiplied by three to the power of two. Then for step two of the build-up method you would build the lowest common multiple from one of the numbers. Beginning with 24 = two to the third power multiplied by three compare it to the prime factorization of 36 = two to the power of two multiplied by three to the power of two. Because the second set has more threes, build up the two to the power of three times three to have the same number of threes as two to the power of two times three to the power of two making the lowest common multiple two to the third power times three to the second power. If there are more than two numbers for which the lowest common multiple is to be found then continue to compare and build with each subsequent number.
This way to figure out the least common multiple could get very confusing to some people. This way is very elementary to us young adults and people that have some education. If you would to present this to children at the elementary level this method could take some time to explain this. All of these methods can also be applied to find the Greatest Common Factor and the Lowest Common Multiple.
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