Answer:
If the two numbers have a highest common factor of 6 , then we can write one number as 6∗a and the other as 6∗b , where a and b are integers. We also know that the product of the two numbers is 360 , so we can write
6∗a∗6∗b=360
or
36∗ab=360
which after dividing both sides by 36 gives us
which after dividing both sides by 36 gives usab=10
The only positive integer solutions for that are
The only positive integer solutions for that area=1,b=10
and
a=2,b=5
which means our possible pairs are 6,60 and 12,30
For both pairs, the LCM is easily seen to be 60.
