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

(1) Greatest common factor of x and y is 10.

(2) The least common multiple of x and y is 180.

You need both statements to come up with answer. I just can't come up with it. Thanks for your help.

Relevance

I have three sets of solutions:

10, 180

20, 90

30, 60

xy = 1800

GCF = 10 = 2 * 5

=> x,y have 2,5 as their common factors(1)

LCM = 180 = 2 * 3^2 * 5

=> either x or y is a multiple of 3(2)

since(1) and (2), only x or only y is a multiple of 3, otherwise they must have 3 as their common factor

thus x = 2 * 5 ; y = 2 * 5 * 3^2 , x * y = 1800 ( or x = 2 * 5 * 3^2 and y = 2 * 5)

• Tim P.
Lv 5

Use prime factorizations.

The GCF of 10 means that the list of factors for each number will include a 2 and a 5, but no other common factors.

The LCM of 180 means that the total list of factors (excluding duplicates) will be 2, 2, 3, 3, 5

Since you know that you've excluded a 2 and a 5 (because they are the only duplicates), the factors for the product of x and y are 2, 2, 2, 3, 3, 5, 5; which multiply to 1800.

If you multiply the less common multiple and the greatest common factor, you will have xy.

Ana

gcf(x,y) . lcm(x,y) = 10 . 180 = 1800

we have a theorem that says that x.y = 1800 too.

The we don't have a unique solution for x and y. Any numbers x and y integer positive that x.y = 1800.

For example: (90,20), (18,100), (30,60) ...

Remember that you will have 2 min but you can think more of a due question if you think less of another one.

Remember this:

ab = mD

Ana

• Dave
Lv 6

x = 10

y = 180

xy = 1800