Question

If a = 2³ ✕ 3, b = 2 ✕ 3 ✕ 5, c = 3ⁿ ✕ 5 and LCM (a, b, c) = 2³ ✕ 3² ✕ 5, then n =

Options

• 1

• 2

• 3

• 4

Answer 1

LCM (a,b,c)= `2^2xx3^2xx5` ……(I)

We have to find the value for n

Also

`a= 2^3xx3`

`b=2xx3xx5`

`c=3^nxx5`

We know that the while evaluating LCM, we take greater exponent of the prime numbers in the factorization of the number.

Therefore, by applying this rule and taking  ` n ≥ 1` we get the LCM as

LCM `(a,b,c)= 2^1xx3^nxx5` ……(II)

On comparing (I) and (II) sides, we get:

`2^3xx3^2xx5=2^3xx3^nxx5`

n=2

Hence the correct choice is (b).