Step 1a

Certainly, let’s find the least common multiple (LCM) of 32 and 68 using the prime factorization method.

Prime factorization of 32:

\$ 32 = 2^5 \$

Prime factorization of 68:

\$ 68 = 2^2 * 17 \$.

Explanation: Let’s break down both numbers into their prime factors.

Step 1b

Identify the highest power of each prime factor:

The highest power of 2 is \$2^5\$.

The highest power of 17 is \$17^1\$.

Explanation: In this context, we denote the greatest exponent of prime factors.

Step 1c

Multiply these highest powers together:

LCM(32, 68) = \$ 2^5 * 17^1 = 32 * 17 \$ = 544

So, the least common multiple of 32 and 68 using the prime factorization method is 544.

Explanation: Let’s multiply the highest powers that have each number. Then we get 544.