Product of X and Y

[chieftang]

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

[xtremecoder007]

is it C? both are required to solve the question.

[rijul007]

This is a very straight-forward question.
It is a property of nos that
the product of two numbers is equal to the product of its GCD and LCM.


Let me prove it to you through this example..
GCD = 15
LCM = 180

GCD = 15
this means
X = 15x
Y = 15y
where x and y dont have any common divisors

LCM = 180
LCM is the product of distinct factors
LCM = 15xy
15xy = 180
xy = 12

X*Y = 15x*15y = 15*15*12

LCM*GCD = 15*180 = 15*15*12

X*Y = LCM*GCD

[mj78ind]

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