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If n can be expressed as p 2q 3 , where p and q are distinct positive

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Bunuel
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If n can be expressed as p 2q 3 , where p and q are distinct positive [#permalink] If n can be expressed as p 2q 3 , where p and q are distinct positive   06 Aug 2017, 00:59
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If n can be expressed as p^2*q^3, where p and q are distinct positive integers greater than 1, what is value of the LCM of p and q?

(1) n is divisible by 9 and 8.
(2) 400 < n < 500
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Luckisnoexcuse
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Re: If n can be expressed as p 2q 3 , where p and q are distinct positive [#permalink] If n can be expressed as p 2q 3 , where p and q are distinct positive   06 Aug 2017, 05:16
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Bunuel wrote:
If n can be expressed as p^2*q^3, where p and q are distinct positive integers greater than 1, what is value of the LCM of p and q?

(1) n is divisible by 9 and 8.
(2) 400 < n < 500


(1) n can be 72 (p=3,q=2), 16*27 (p=4,q=3), 36*64 (p=6,q=4)..LCM value is different

(2)
if q =2 then p cannot take any value as
7^2 = 49 * 8 <400
and 8^2 = 64 * 8>500
if q = 3 then p can take 4 making n = 432

if q = 4 then p cannot take any value as
2^2 = 4*64 <400
3^2 = 9*64>500
P cannot take any value apart from 4
if p=2 then q cannot take any value fulfilling the criteria
if p=3 then q cannot take any value fulfilling the criteria
if p =5 then q cannot take any value fulfilling the criteria
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Re: If n can be expressed as p 2q 3 , where p and q are distinct positive [#permalink] If n can be expressed as p 2q 3 , where p and q are distinct positive   30 Jun 2021, 06:01
Hey Bunuel,
Can you please post the solution to this.
I can't think of a solution that be done within 2 minutes.
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Re: If n can be expressed as p 2q 3 , where p and q are distinct positive [#permalink]
30 Jun 2021, 06:01
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Bunuel
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