The product of three consecutive natural numbers is divisible by: - Vidyadip

MCQ

The product of three consecutive natural numbers is divisible by:

A
3
B
8
C
6
✓
(A) and (C) both

✓

Answer

Correct option: D.

(A) and (C) both

d. (A) and (C) both
Solution:
Let n, n + 1, n + 2 be three consecutive natural numbers and P(n) be their product. Then,
P(n) = n(n + 1)(n + 2)
We have,
P(1) = 1 × 2 × 3 = 6, which is divisible by 3 and 6.
P(2) = 2 × 3 × 4 = 24, which is divisible by 3, 8 and 6.
P(3) = 3 × 4 × 5 = 60, which is divisible by 3 and 6.
P(4)= 4 × 5 × 6 = 120, which is divisible by 3, 8 and 6.
Hence, P(n) is divisible by 3 and 6 for all n ∈ N.

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