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 of the numbers 24, 36, and 60.

Prime factorization of 24:
\[ 24 = 2 \times 12 = 2 \times 2 \times 6 = 2 \times 2 \times 2 \times 3 = 2^3 \times 3 \]

Prime factorization of 36:
\[ 36 = 2 \times 18 = 2 \times 2 \times 9 = 2 \times 2 \times 3 \times 3 = 2^2 \times 3^2 \]

Prime factorization of 60:
\[ 60 = 2 \times 30 = 2 \times 2 \times 15 = 2 \times 2 \times 3 \times 5 = 2^2 \times 3 \times 5 \]

Step 2: Finding the LCM using prime factors:
The LCM is found by taking the highest power of each prime factor that appears 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 \( 5^1 \) (from 60).

Step 3: LCM of 24, 36, and 60:
The LCM is the product of the highest powers of all the prime factors:
\[ \text{LCM} = 2^3 \times 3^2 \times 5 \]

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