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Question

Find two natural numbers whose difference is 66 and the least common multiple is 360.

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Solution

Let the two numbers be x and x+66.
Since, the LCM is 360, there must be 5,2 and 3 as the prime factors of the two numbers.
So, one pair is 24 & 90, because 9024=66.
Also, 24=2×2×2×3
90=2×3×3×5
LCM=2×2×2×3×3×5=360.
So, the numbers are 24 and 90.

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