How do you make a list of possible pairs of numbers that have a LCM of 48?

1 Answer
Shwetank Mauria
Dec 5, 2016

14 such pairs, which are (1,48),(2,48),(3,48),(4,48),(6,48)

(8,48),(12,48),(16,48),(24,48},(48,48),(3,16),(6,16),(12,16),(24,16)

Explanation:

First of all pairing 48 with all of its factors i.e. {1,2,3,4,6,8,12,16,24,48}. This gives us 10 such pairs.

We can also add (3,16), as they are relatively coprime. Further, selecting multiples of 3 will also lead to the pairs (6,16),(12,16),(24,16)

Hence in all 14 such pairs, which are

(1,48),(2,48),(3,48),(4,48),(6,48),(8,48),(12,48),(16,48),(24,48},(48,48),(3,16),(6,16),(12,16),(24,16)

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