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The LCM (Least Common Multiple) of two numbers is the smallest number that is a multiple of both of them.

To find the LCM of 9 and 15, we can list their multiples and find the smallest one that they have in common:

Multiples of 9: 9, 18, 27, 36, 45, 54, 63, 72, 81, 90, 99, 108, 117, 126, 135, 144, 153, 162, 171, 180, …

Multiples of 15: 15, 30, 45, 60, 75, 90, 105, 120, 135, 150, 165, 180, …

We can see that the first multiple they have in common is 45. Therefore, the LCM of 9 and 15 is 45.

Another way to find the LCM is to use the prime factorization method. We can write:

9 = 3 Ã— 3 15 = 3 Ã— 5

The LCM is the product of the highest powers of all prime factors involved. In this case, we have one prime factor of 3 and one prime factor of 5, so:

LCM(9, 15) = 3 Ã— 3 Ã— 5 = 45

Either method gives the same result, which is the LCM of 9 and 15 is 45.