# How do you find the least common multiple of 10, 2, and 15?

30

Since ten is less than fifteen, the multiple must be greater than ten. The final digit of any whole number multiple of ten will be 0.

Since 2 will be an LCM factor, it cannot be an odd number.

Thus, 30 is the LCM.

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To find the least common multiple (LCM) of 10, 2, and 15, you can follow these steps:

- Write the prime factorization of each number.
- Identify the highest power of each prime factor that appears in any of the factorizations.
- Multiply these highest powers together to find the LCM.

In this case:

- Prime factorization of 10 is (2 \times 5).
- Prime factorization of 2 is (2).
- Prime factorization of 15 is (3 \times 5).

Identifying the highest powers:

- Highest power of 2 is (2^1).
- Highest power of 3 is (3^1).
- Highest power of 5 is (5^1).

Multiplying these highest powers together: [ LCM(10, 2, 15) = 2^1 \times 3^1 \times 5^1 = 2 \times 3 \times 5 = 30 ]

So, the least common multiple of 10, 2, and 15 is 30.

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