chieftang wrote:What is the product of X and Y ?
1. The greatest common factor of X and Y is 15
2. The least common multiple of X and Y is 180
Source: Original
I like Rijul007's approach, here is another one. This is more on the intuitive side:
1. GCF = 15, the numbers could be 15, 30; 15,45 etc. Hence insufficient
2. LCM = 180 the numbers could be 2,180; 15,180 etc. hence insufficient
Combining 1 and 2. We know both the numbers should have 3 and 5 or GCF can not be 15, note there can not be any more common terms between the numbers or GCF > 15. Now 180 = (2^2)*(3^3)*5, we know the numbers have 3 and 5 and nothing else common. Hence, 2^2 has to go to one number the remaining 3 can go to either number. Thus the numbers could be:
15, 12*15 or
3^2*5, 4*15
In either case the product of the numbers is (2^2)*(3^3)(5^2)
Hope this is not very confusing
