Another example:
Let's find the LCM of 10 and 15.
Method 1: Listing Multiples
Multiples of 10: 10, 20, 30, 40, 50, ...
Multiples of 15: 15, 30, 45, 60, ...
From the lists above, we see that 30 is the smallest multiple that appears in both lists, so the LCM of 10 and 15 is 30.
Method 2: Prime Factorization
Prime factorization of 10: 2 * 5
Prime factorization of 15: 3 * 5
To find the LCM, we multiply the highest powers of all prime factors. In this case, the highest power of 2 is 1, the highest power of 3 is 1, and the highest power of 5 is 1, so the LCM of 10 and 15 is 2 * 3 * 5 = 30.
So, in either method, we find that the LCM of 10 and 15 is 30.