Question

If a = 23×3, b = 2×3×5, c = 3n×5and LCM

(a, b, c) = 23×32×5, then n = ____​

Answer 1

n=2

LCM=(abc)=2^2×3^2×5....(1)

we have to find the value for n

also,

a=2^3×3

b=2×3×55

c=3n×5

we know that the while evaluating 1cm

we take greater exponent of the prime numbers in the factorisation of the number

by applying this rule and taking n>_1we get LCM as

LCM (abc)=2^1×3^n×5....(2)

on comparing 1and2 sides,we get

2^2×3^2×5=2^2×3^n×5

n=2