Question

The $LCM$ of the numbers 12, 15 and 21 will be:

• A. 60
• B. 120
• C. 210
• D. 420

Hint:

For finding $LCM$, always use the highest powers of all prime factors present in the numbers.

Answer 1

The Correct Option is C

Step 1: Prime factorization
- $12 = 2^2 \times 3$
- $15 = 3 \times 5$
- $21 = 3 \times 7$

Step 2: Take highest powers of all primes
\[ LCM = 2^2 \times 3 \times 5 \times 7 \] \[ LCM = 4 \times 3 \times 5 \times 7 = 420 \]

Step 3: Re-check options
The $LCM(12, 15, 21) = 420$.
So, the correct answer is option (D).