What is the greatest common multiple of 15, 75 and 90?

The greatest common multiple is not a valid mathematical term. However, I can help you find the Greatest Common Divisor (GCD) or the Least Common Multiple (LCM).

The GCD of 15, 75, and 90 is the largest number that divides all of them without leaving a remainder.

Here are the steps to find the GCD:

1. First, find the prime factors of each number.

   • The prime factors of 15 are 3 and 5.
   • The prime factors of 75 are 3, 5, and 5.
   • The prime factors of 90 are 2, 3, 3, and 5.

2. Next, find the common prime factors.

   • The common prime factors are 3 and 5.

3. Multiply the common prime factors.

   • 3 * 5 = 15

So, the GCD of 15, 75, and 90 is 15.

If you meant to ask for the Least Common Multiple (LCM), it is the smallest number that all three numbers divide evenly into.

Here are the steps to find the LCM:

1. List the prime factors of each number.

   • The prime factors of 15 are 3 and 5.
   • The prime factors of 75 are 3, 5, and 5.
   • The prime factors of 90 are 2, 3, 3, and 5.

2. For each prime number, count the number of times it appears in each list, and take the maximum count.

   • The maximum count of 2 is 1 (from 90).
   • The maximum count of 3 is 2 (from 90).
   • The maximum count of 5 is 2 (from 75).

3. Multiply these maximum counts of prime factors.

   • 2^1 * 3^2 * 5^2 = 2 * 9 * 25 = 450

So, the LCM of 15, 75, and 90 is 450.