If a=5^13×7, b=3×5^25×7^6, c=5^n×7^4 . . .

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

Doubt by Muskan

Solution :

a=5¹³×7
b=3×5²⁵×7⁶
c=5ⁿ×7⁴

^{LCM(a,b,c) =}3×5ⁿ×7⁶^{— (1)
LCM (a,b,c) =}3×5³¹×7⁶ ^{— (2) [Given]

From (1) and (2)}

3×5ⁿ×7⁶ = 3×5³¹×7⁶
5ⁿ = 5³¹
n=31

Hence, (a) 31, would be the correct option.

Class 10