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To find the least common multiple (LCM) of 16 and 56, we can start by finding the prime factorization of each number:
16 = 2 x 2 x 2 x 2 56 = 2 x 2 x 2 x 7
Then, we can find the LCM by taking the product of the highest power of each prime factor. In this case, the prime factors are 2 and 7, and the highest power of 2 is 4 (from 2 x 2 x 2 x 2), while the highest power of 7 is 1 (since 7 does not appear in the prime factorization of 16). Thus, the LCM of 16 and 56 is:
LCM(16, 56) = 2^4 x 7 = 112
Therefore, the least common multiple of 16 and 56 is 112.