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Question

# The L.C.M of two numbers is six - times their HCF. If their difference between L.C.M and H.C.F is 60 and one of the two numbers is 36, find the other number.

A
14
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B
18
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C
22
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D
24
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Solution

## The correct option is D 24One number = 36 (given) L.C.M of two numbers = 6 (H.C.F of two numbers) ----- (i) L.C.M - H.C.F = 60 -------- (ii) From (i) 6 H.C.F - H.C.F = 60 5 H.C.F = 60 H.C.F = 605 = 12 L.C.M = 6 (H.C.F) = 6 × 12 = 72 H.C.F × L.C.M = Product of two numbers 12 × 72 = 36 × Second number Second number = 12×7236 Second number = 24

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