What is the least common multiple of the denominators for the two fractions 16 and 58?

To find the least common multiple (LCM) of the denominators 16 and 58, we first need to consider the prime factorization of each number.

The prime factorization of 16 is:

• 16 = 2 × 2 × 2 × 2 = 2⁴

For 58, the prime factorization is:

• 58 = 2 × 29

Now, to find the LCM, we take the highest power of each prime factor that appears in the factorizations:

• From 16, we take 2⁴.
• From 58, we take 29¹.

Thus, the LCM is:

• LCM = 2⁴ × 29¹ = 16 × 29 = 464

Therefore, the least common multiple of the denominators 16 and 58 is 464.