Find the LCM of 48 and 60.

To find the least common multiple (LCM) of 48 and 60, we can use several methods. Here’s one approach using prime factorization:

First, we can factor both 48 and 60 into primes:

• 48 = 2^4 x 3^1
• 60 = 2^2 x 3^1 x 5^1

Next, we can find the highest power of each prime that appears in either factorization. To do this, we look for the largest exponent of each prime that appears in either factorization:

• 2^4 appears in 48, and 2^2 appears in 60. So we take the larger exponent, 2^4, to include all of the factors of 2 in both numbers.
• 3^1 appears in both factorizations, so we include it once.
• 5^1 appears in 60, but not in 48, so we include it.

Multiplying these prime factors together, we get the LCM: LCM(48, 60) = 2^4 x 3^1 x 5^1 = 240

Therefore, the LCM of 48 and 60 is 240.