I am thinking of two numbers. The greatest common factor is 3. The least common multiple is 90. What are my two numbers

Question

I really need help on this  can someone help me.

Answer 1

It is true that the LCM times the GCF equals the product of the two numbers.

90*3=270

270=3*3*3*2*5

there are several answers depending on how you group the factors

(3*3*5)(3*2)=45*6 so 6 and 45 are the numbers (1 solution)

(3*3)(3*2*5)=9*30 so 9 and 30 are the numbers (another solution)

(3*5)(3*3*2)=15*18 so 15 and 18 are the numbers (another solution)

(3)*(3*3*2*5)=3*90 so 3 and 90 are the numbers  (another solution albeit trivial)