Question

The smallest positive number which is divisible by the numbers 2, 3, 4, 5, 6, 7 is

• A. 840
• B. 1260
• C. 210
• D. 420

Hint:

To find smallest number divisible by multiple numbers, calculate LCM using highest powers of each prime factor.

Answer 1

The Correct Option is D

We are asked to find the smallest number divisible by: 2, 3, 4, 5, 6, 7
This is the LCM (Least Common Multiple) of these numbers. Step 1: Find prime factorizations
2 = 2
3 = 3
4 = \( 2^2 \)
5 = 5
6 = \( 2 \times 3 \)
7 = 7 Step 2: Take highest powers of all primes
LCM = \( 2^2 \times 3 \times 5 \times 7 = 4 \times 3 \times 5 \times 7 = 420 \)