and LCM (a, b, c) = 3780, then x is equal to

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Solution

Q.
If a = $2 ² \times 3 ˣ, b = 2 ² \times 3 \times 5, c = 2 ² \times 3 \times 7$ and LCM (a, b, c) = 3780, then x is equal to:

1 1

2 2

3 3

4 0

Ans.
(3)

If LCM (a,b,c) = 3780
By prime factorisation of 3780

$3780 = 2^{2} \times 3^{3} \times 5 \times 7 L C M (a, b, c) = 2^{2} \times 3^{3} \times 5 \times 7 (i) a = 2^{2} \times 3^{x}; b = 2^{2} \times 3 \times 5; c = 2^{2} \times 3 \times 7 L C M (a, b, c) = 2^{2} \times 3^{x} \times 5 \times 7 (i i) C o m p a r i n g (i) a n d (i i), w e g e t 𝑥 = 3$

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