Question 78172
let x=1st number, y=second number

Since the LCM is the product of the 2 numbers divided by the GCF we have

LCM: {{{180=(x*y)/12}}}

So multiply both sides by 12

{{{x*y=2160}}}

So the product of the 2 numbers is 2160. We know that in order to have a GCF of 12, the lowest number is 12. So lets try x=12

{{{12y=2160}}} Plug in x=12

{{{y=180}}} Divide both sides by 12

So our second number is 180

Now lets find the GCF and the LCM between these 2 numbers:


*[invoke find_greatest_common_factor 180, 12]


Now lets find the LCM

*[invoke least_common_multiple 180, 12]

We got lucky on our first try. So it turns out that the two numbers are

12,180