Question 1185885
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The LCM of the three number is 900 = (2^2)(3^2)(5^2).<br>
The LCM of 60 and 150 is 300 = (2^2)(3^1)(5^2).<br>
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.<br>
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.<br>
ANSWERS: 90, 180, and 450<br>