### Instruction: Find the least common multiple of 36 and 132.### Response: To find the least common multiple of two numbers, I need to find the smallest positive integer that is a multiple of both numbers.
One way to do that is to use prime factorization and compare the powers of each prime factor in the two numbers.
I can write 36 as 2^2 * 3^2 and 132 as 2^2 * 3^1 * 11^1.
To find the least common multiple, I need to take the highest power of each prime factor that appears in either number.
That means I need 2^2, 3^2, and 11^1 in the least common multiple.
Multiplying these factors together, I get 2^2 * 3^2 * 11^1 = 4 * 9 * 11 = 396.
Therefore, the least common multiple of 36 and 132 is 396.