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Re: LCM and GCD- can som1 suppose any safe and easy method? [#permalink]
07 Jun 2011, 09:44
This post received KUDOS
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.