# What is the LCM of #21m^2n#, #84mn^3#?

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The LCM of 21m^2n and 84mn^3 is 84m^2n^3.

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To find the least common multiple (LCM) of the given expressions, we need to factorize each expression into its prime factors and then determine the highest power of each prime factor that appears in either expression.

The prime factorization of (21m^2n) is (3 \times 7 \times m^2 \times n), and the prime factorization of (84mn^3) is (2^2 \times 3 \times 7 \times m \times n^3).

To find the LCM, we take the highest power of each prime factor that appears in either expression:

- The highest power of 2 is (2^2).
- The highest power of 3 is (3).
- The highest power of 7 is (7).
- The highest power of (m) is (m^2).
- The highest power of (n) is (n^3).

Therefore, the LCM of (21m^2n) and (84mn^3) is (2^2 \times 3 \times 7 \times m^2 \times n^3), which simplifies to (84m^2n^3).

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