What is the LCM of 6 and 32?

To find the Least Common Multiple (LCM) of 6 and 32, we can follow a simple method using the prime factorization of each number.

First, let’s factor each number:

• 6 can be factored into prime factors as: 2 × 3
• 32 can be factored into prime factors as: 2 × 2 × 2 × 2 × 2 (or 2⁵)

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

• The prime factor 2 appears in 6 as 2¹ and in 32 as 2⁵. The highest power of 2 is 2⁵.
• The prime factor 3 appears only in 6 as 3¹. The highest power of 3 is 3¹.

Now, we multiply these together to find the LCM:

LCM = 2⁵ × 3¹ = 32 × 3 = 96

Thus, the LCM of 6 and 32 is 96.