Number theory gcd lcm posiible pairs

#1

How many ordered pairs of two numbers are possible such that LCM = 120 and GCD = 2?

#2

@kunalsaini8950 I believe there are 3.
They are : 2,120 , 6,40, 10,24

#3

In order to find the number of pairs with a given GCD and LCM, I find the number n of prime factors in LCMGCD. The number of pairs is equal to 2n.

Example: GCD=2 and LCM=120
LCM/GCD=60=2power2∗5∗3
therefore we have 2power3 (we have 3 prime factors) pairs.

#4

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