To find the least common multiple (LCM) of 2b^2 and 6c^3, we first need to factorize both terms. The prime factorization of 2b^2 is 2 * b * b, and the prime factorization of 6c^3 is 2 * 3 * c * c * c. To find the LCM, we take the highest power of each prime factor that appears in either term, which gives us 2 * 3 * b^2 * c^3 = 6b^2c^3. Therefore, the LCM of 2b^2 and 6c^3 is 6b^2c^3.
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