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Re: LCM and GCD- can som1 suppose any safe and easy method? [#permalink]

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07 Jun 2011, 10:44

3

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Expert's post

dimri10 wrote:

If the LCM of A and 12 is 36, what are the possible values of A?

Think of what LCM means before going ahead. If I say LCM of two numbers is \(36 (= 4*9 = 2^2 * 3^2)\), it means that at least one of them must have a \(2^2\) and at least one of them must have a \(3^2\) (It is not possible that both numbers have just 3 because then, the LCM would have just 3, not 9)

If one number is \(12 (= 2^2 * 3)\), the other number A must have \(3^2\) since 12 doesn't have it. So minimum value of A will be 9. A can also have a 2 or a \(2^2\) so other possible values are \(18 (=9*2)\) and \(36 (= 9*2^2)\) Also, A cannot have any other factors since if it did, then the LCM would have to have that factor too. _________________

Re: LCM and GCD- can som1 suppose any safe and easy method? [#permalink]

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15 Jan 2016, 01:24

VeritasPrepKarishma wrote:

dimri10 wrote:

If the LCM of A and 12 is 36, what are the possible values of A?

Think of what LCM means before going ahead. If I say LCM of two numbers is \(36 (= 4*9 = 2^2 * 3^2)\), it means that at least one of them must have a \(2^2\) and at least one of them must have a \(3^2\) (It is not possible that both numbers have just 3 because then, the LCM would have just 3, not 9)

If one number is \(12 (= 2^2 * 3)\), the other number A must have \(3^2\) since 12 doesn't have it. So minimum value of A will be 9. A can also have a 2 or a \(2^2\) so other possible values are \(18 (=9*2)\) and \(36 (= 9*2^2)\) Also, A cannot have any other factors since if it did, then the LCM would have to have that factor too.

Thanks Karishma. Your solution is very clear and in simple way. I didn't understand the complicated solution prepared by Manhattan. Their prime columns technique is good but solution explanation was confusing.

gmatclubot

Re: LCM and GCD- can som1 suppose any safe and easy method?
[#permalink]
15 Jan 2016, 01:24

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