# What is the least common multiple of 32, 15, and 36?

The least common multiple (LCM) can be found by taking the power of the highest power used of each prime after examining the prime factorization of all of our given values. This allows us to make sure that the prime factorization of our LCM contains the prime factorizations of all of our initial values, i.e., it is divisible by each.

Given the foregoing, the LCM will be

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To find the least common multiple (LCM) of 32, 15, and 36, you can start by finding the prime factorization of each number:

- 32 = 2^5
- 15 = 3 * 5
- 36 = 2^2 * 3^2

Then, identify the highest power of each prime factor that appears in any of the factorizations:

- The highest power of 2 is 5 (from 32).
- The highest power of 3 is 2 (from 36).
- The highest power of 5 is 1 (from 15).

Multiply these highest powers together to find the LCM:

[LCM = 2^5 * 3^2 * 5^1] [LCM = 32 * 9 * 5] [LCM = 1440]

So, the least common multiple of 32, 15, and 36 is 1440.

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