Three whole numbers have their L.C.M as 180 and their H.C.F equal to 3. Two of the numbers are 45 and 60. Find the third number. Please show working. Thanks

Question

Highest common factor and Least common multiple

Answer 1

The three numbers can be represented by 3a, 3b, 3c, LCM=3abc=180, abc=60.

a=15 and b=20, (45 and 60). 15=3×5, 20=4×5 so LCM of 15 and 20 is 60, c=60/60=1.

So the numbers are 3, 45, 60.