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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