If the LCM of P and 18 is 36 and the HCF

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Solution

Q.
If the LCM of P and 18 is 36 and the HCF of P and 18 is 2, then P equals:

1 2

2 3

3 1

4 4

Ans.
(4)

$W e k n o w t h a t L C M (a, b) \times H C F (a, b) = a \times b$

$\Rightarrow L C M (P, 18) \times H C F (P, 18) = P \times 18$

$\Rightarrow 36 \times 2 = P \times 18 \Rightarrow 72 = 18 P$

$\Rightarrow P = 72 \div 18 = 4$

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