Find two pairs of numbers a and b such that GCF(a,b)=153 and LCM(a,b)=918 How do I figure out the a and b?

Question

I need to find the two numbers that the GCF=153 and same for the LCM.  This pair of numbers are different?  I know that a*b=GCF*LCM but I do not know how to solve for the set of numbers that make the GCF and LCM.  I am looking for formula and help.  Thanks!

Answer 1

LCM=918=2*3*3*3*17

GCF=153=3*3*17

both a and b must contain 3*3*17

a=3*3*17

b=3*3*17 so far...

this leaves 2 and 3

put one number with a and put the other number with b

a=2*3*3*17=306

b=3*3*3*17=459

 

sometimes you have to repeat this using trial and error

example:

36 and 45 are the numbers

LCM=180

GCF=9

10=2*2*3*3*5

9=3*3

both numbers contain 3*3

a=3*3

b=3*3

this leaves 2, 2, and 5

putting 2 with a and putting 10 with b doesn't work

put 4 with a and put 5 with b

a=4*3*3=36

b=5*3*3=45