If a=2^2×3^x, b=2^2×3×5, c=2^2×3×7 and . . .

Question : If a=2²×3^x, b=2²×3×5, c=2²×3×7 and LCM (a, b, c) = 3780, then x is equal to

(A) 1
(B) 2
(C) 3
(D) 0

CBSE Sample Question Paper 2025-2026

Solution : 

a=2²×3^x

b=2²×3×5

c=2²×3×7

LCM (a,b,c) = 2²×3^x×5×7 — (1) 

LCM (a,b,c) = 3780 (Given)
LCM (a,b,c) = 2²×3³×5×7 — (2) 

From (1) and (2) 
2²×3^x×5×7=2²×3³×5×7
3^x=3³

Clearly x=3

So, (C) 3, would be the correct option.

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 Similar Question : 

If a=5¹³×7, b=3×5²⁵×7⁶, c=5ⁿ×7⁴ and LCM (a,b,c) = 3×5³¹×7⁶, then n=?
(a) 31

(b) 25
(c) 13
(d) 34

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