Question 1185885: the GCD of three numbers is 30 and their LCM is 900. if two of te numbers are 150 and 60 find the other possible numbers
Answer by greenestamps(13198)   (Show Source):
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The LCM of the three number is 900 = (2^2)(3^2)(5^2).
The LCM of 60 and 150 is 300 = (2^2)(3^1)(5^2).
Since the GCD of the three numbers is 30, the third number must be a multiple of 30, and it must contain an additional factor of 3. So the third number is a multiple of 90.
Finish the problem informally, simply by finding which multiples of 90 make the LCM 900 -- that is, find the multiples of 90 that are factors of 900.
ANSWERS: 90, 180, and 450
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