What is the least common multiple of 18, 9 and 7?

The least common multiple (LCM) of 18, 9, and 7 can be found by first finding the prime factorization of each number.

1. Prime factorization of 18: 2 * 3^2
2. Prime factorization of 9: 3^2
3. Prime factorization of 7: 7

Next, for each prime number, take the highest power that appears in any of the factorizations, and multiply those together.

• The prime numbers are 2, 3, and 7.
• The highest power of 2 that appears is 2^1 (from 18).
• The highest power of 3 that appears is 3^2 (from both 18 and 9).
• The highest power of 7 that appears is 7^1 (from 7).

Multiply these together to get the LCM:

LCM = 2^1 * 3^2 * 7^1 = 2 * 9 * 7 = 18 * 7 = 126

So, the least common multiple of 18, 9, and 7 is 126.