Question
Three numbers are in the ratio of 2 : 5 : 7, and their least common multiple (LCM) is 1050. Determine their greatest common divisor (GCD).
The correct answer is
15
The numbers are in the ratio 2 : 5 : 7. Their LCM is 1050. We can express these numbers as 2x, 5x, and 7x. The LCM of 2x, 5x, and 7x is the LCM of 2, 5, and 7, multiplied by x. We know that the LCM of 2, 5, and 7 is 70, so 70x = 1050. Thus, x = 15. The three numbers are 30, 75, and 105. The GCD of 30, 75, and 105 is 15.
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