What is the least common multiple of 135 and 468?
I need to find the smallest positive integer that is a multiple of both 135 and 468. One way to do this is to factorize both numbers and then take the highest power of each prime factor. 135 = 3^3 * 5 and 468 = 2^2 * 3^2 * 13. The highest power of 2 is 2^2, the highest power of 3 is 3^3, the highest power of 5 is 5^1, and the highest power of 13 is 13^1. So the least common multiple is 2^2 * 3^3 * 5 * 13. To find the numerical value, I can use a calculator or do the arithmetic by hand. 2^2 = 4, 3^3 = 27, 5 * 13 = 65. 4 * 27 * 65 = 7020. 