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# If P and Q are positive integers, is P*Q divisible by 63?

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Current Student
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Schools: Boston U '20 (M)
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If P and Q are positive integers, is P*Q divisible by 63?  [#permalink]

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28 Jan 2017, 18:36
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45% (medium)

Question Stats:

64% (01:21) correct 36% (01:27) wrong based on 101 sessions

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If $$P$$ and $$Q$$ are positive integers, is $$P*Q$$ divisible by 63?

(1)GCD of $$P$$ and $$Q$$ is 6.
(2)LCM of $$P$$ and $$Q$$ is 1260.

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Re: If P and Q are positive integers, is P*Q divisible by 63?  [#permalink]

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28 Jan 2017, 20:13
For any 2 integers P & Q P*Q = (LCM of P & Q)*(GCD of P & Q)

(1) From this statement we can say P*Q ia divisible by 6 but nothing more than that. Hence Insufficient.
(2) From this statement: P*Q = 1260*GCD. Now 1260 alone is divisible by 63. So P*Q is divisible irrespective of the GCD. Hence Sufficient.

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Re: If P and Q are positive integers, is P*Q divisible by 63?  [#permalink]

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15 Nov 2018, 04:52
It is a good question and one might do it wrong if he is in a hurry.

From the number properties
P*Q = LCM(P,Q) * GCD(P,Q)

Thus from Stat -1 we have only GCD --> clearly it is not sufficient to answer the question
Stat-2 we are given LCM 1260 which is equal to 63 *20 if simplify it in terms of 63. --> clearly p*q is divisible by 63 as 63 is present in either in P or in Q or in both of them.
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Re: If P and Q are positive integers, is P*Q divisible by 63?  [#permalink]

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26 Nov 2019, 17:11
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Re: If P and Q are positive integers, is P*Q divisible by 63?   [#permalink] 26 Nov 2019, 17:11
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