L.C.M. of 12, 24, and 36 is ____?

• A. 36
• B. 24
• C. 72
• D. 108

To find the least common multiple (L.C.M.) of the numbers 12, 24, and 36, we can use the prime factorization method.

Step 1: Prime Factorization

First, let's break down each number into its prime factors:

• 12 = 2² × 3
• 24 = 2³ × 3
• 36 = 2² × 3²

Step 2: Identify the Highest Powers

Next, we take the highest power of each prime factor:

• For 2: the highest power is 2³ (from 24)
• For 3: the highest power is 3² (from 36)

Step 3: Calculate the L.C.M.

Now, we multiply these highest powers together:

L.C.M. = 2³ × 3² = 8 × 9 = 72

Final Answer

The least common multiple of 12, 24, and 36 is 72. Therefore, the correct option is C. 72.

To find the least common multiple (L.C.M.) of the numbers 12, 24, and 36, we can use the prime factorization method.

Step 1: Prime Factorization

• 12 = 2² × 3
• 24 = 2³ × 3
• 36 = 2² × 3²

Step 2: Identify the Highest Powers

Next, we take the highest power of each prime factor:

• For 2: the highest power is 2³ (from 24)
• For 3: the highest power is 3² (from 36)

Step 3: Calculate the L.C.M.

Now, we multiply these highest powers together:

L.C.M. = 2³ × 3² = 8 × 9 = 72

Final Answer

The least common multiple of 12, 24, and 36 is 72. Therefore, the correct option is C. 72.