What is the LCM of sets of numbers 8, 12, 16, 3?

To find the Least Common Multiple (LCM) of the numbers 8, 12, 16, and 3, we can follow a systematic approach.

Step 1: Prime Factorization

First, we break down each number into its prime factors:

• 8 = 2 × 2 × 2 = 2³
• 12 = 2 × 2 × 3 = 2² × 3¹
• 16 = 2 × 2 × 2 × 2 = 2⁴
• 3 = 3¹

Step 2: Identify the Highest Powers

Next, we take the highest power of each prime number that appears in the factorizations:

• For 2: the highest power is 2⁴ (from 16)
• For 3: the highest power is 3¹ (from 12 and 3)

Step 3: Calculate the LCM

Now, we multiply these highest powers together to find the LCM:

LCM = 2⁴ × 3¹ = 16 × 3 = 48

Final Result

The LCM of the numbers 8, 12, 16, and 3 is 48.