Question

The LCM of 24, 36 and 60 in terms of their prime factors is :

• A. 2² × 3 × 5
• B. 2³ × 3²
• C. 2³ × 3²× 5
• D. 2³ × 3³× 5

Answer 1

The Correct Option is C

Step 1: Prime factorization of the numbers:
We need to find the prime factorization of each number.
- The prime factorization of 24 is: \( 24 = 2^3 \times 3 \)
- The prime factorization of 36 is: \( 36 = 2^2 \times 3^2 \)
- The prime factorization of 60 is: \( 60 = 2^2 \times 3 \times 5 \)

Step 2: Determine the LCM:
To find the Least Common Multiple (LCM), we take the highest powers of all the prime factors that appear in the prime factorizations of the numbers.
- The highest power of 2 is \( 2^3 \) (from 24).
- The highest power of 3 is \( 3^2 \) (from 36).
- The highest power of 5 is \( 5 \) (from 60).

Thus, the LCM is: \[ \text{LCM} = 2^3 \times 3^2 \times 5 \]

Step 3: Conclusion:
The LCM of 24, 36, and 60 in terms of their prime factors is \( \boxed{2^3 \times 3^2 \times 5} \).