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There r 2 numbers with a LCM of 72 the smaller number is 9 the gcf of the two number is 3 and their sum is between 30 and 40 what is the larger number?
Wiki User
∙ 14y ago
Let the two numbers by A and B with A>B
Both numbers have 3 as a factor therefore write A = 3a, B = 3b = 9
As the LCM is 72 then AB = 72n as the product of the numbers is a multiple of the LCM.
Then 72n = 3a x 9 = 27a : a/n = 72/27 = 8/3.
This equation holds true when a = 8 and n = 3 (or multiples of these two numbers)
When a = 8, A = 3x8 = 24, A + B = 24 + 9 = 33 which is a number between 30 and 40.
The larger number is 24.
Wiki User
∙ 14y ago
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