Number theory

[suhir.kumar]

If x and y are positive integers , what is the value of xy??

(1)The greatest common factor of x and y is 10
(2)The least common multiple of x and y is 180

[shubham_k]

I think the answer should be C.

10 GCD => X/10, Y/10 will be that part of X, Y which are uncommon between the two. This means if we multiply these two with 10, that would give me LCM.

i.e. X*Y/10 = 180 or X.Y=1800. Also we know that gcd*lcm of two integers = product of two integers.

[Birottam Dutta]

The trick in this question is to remember that product of two numbers is equal to the product of their LCM and GCF.

So, by using both statements together, we can arrive at the answer.

Hence, C.

[Anurag@Gurome]

If x and y are positive integers , what is the value of xy??

(1)The greatest common factor of x and y is 10
(2)The least common multiple of x and y is 180

(1)The greatest common factor of x and y is 10.
If x = y = 10, then GCF of x and y = 10. Here xy = 10 * 10 = 100.
If x = 20, y = 10, then GCF of x and y = 10. Here xy = 20 * 10 = 200.
No definite answer; NOT sufficient.

(2) The least common multiple of x and y is 180.
If x = 1, y = 180, then LCM of x and y = 180. Here xy = 1 * 180 = 180.
If x = 10, y = 180, then LCM of x and y = 180. Here xy = 10 * 180 = 1800.
No definite answer; NOT sufficient.

Combining (1) and (2), GCF of x and y = 10 and LCM of x and y = 180
Note: If x and y are two positive integers, then LCM of x, y * GCF of x, y = x * y
So, xy = 10 * 180 = 1800; SUFFICIENT.

The correct answer is C.