Algebra 1: Common Core (15th Edition)

The least common multiple (LCM) is the smallest number that is divisible by all the numbers in question (25, 15, 10). To find the LCM, you can find the prime factorization of all the numbers, which are $5^2$, $5\times3$, and $5\times2$, respectively. Next, you would find the largest occurrence of each number by comparing the prime factorizations. For example, the number 5 occurs the most in the prime factorization of 25. Similarly, the number of 2's and 3's occurs the most in 10 and 15, respectively. Generally, you would continue this process for all prime factors of any of the numbers in question. Now you just multiply the numbers together based on the occurrence of each. In other words, the final result will be $5\times5\times2\times3=150$, because 5 occurs twice so there are 2 fives in the final product, and 2 occurs once as does three, so there are one 2 and one 3 in the final product. Checking our work we see that 150 is divisible by 15, 25 and 10.