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If $a = 2^{3} \times 3$ , $b = 2 \times 3 \times 5, c = 3^{n} \times 5$ and $LCM (a, b, c) = 2^{3} \times 3^{2} \times 5$ , then find n.

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answer is B.

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Detailed Solution

Given,

a = 2^{3} \times 3

b = 2 \times 3 \times 5

c = 3^{n} \times 5

LCM (a, b, c) = 2^{3} \times 3^{2} \times 5

… 1
The factors of a, b and c are as follows:

a = 2^{3} \times 3

b = 2 \times 3 \times 5

c = 3^{n} \times 5

LCM (a, b, c) = 2^{3} \times 3^{n} \times 5

… 2
Equate (1) and (2),

2^{3} \times 3^{2} \times 5 = 2^{3} \times 3^{n} \times 5

⇒

3^{2} = 3^{n}

\Rightarrow n = 2

Therefore, if

a = 2^{3} \times 3

b = 2 \times 3 \times 5, c = 3^{n} \times 5

and

LCM (a, b, c) = 2^{3} \times 3^{2} \times 5

, then the n is 2.
Hence, option 2 is correct.

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