GCF and LCM finding two pairs

Question

Find two pairs of numbers a and b such that GCF(a,b) = 153 and LCM(a,b) = 918.

 

I believe the LCM(306,459) based a previous question but I need to know how to figure out the GCF(a,b)= 153.  I need to know the formula, process.

 

Thank you!

Answer 1

Start by finding all the prime factors of the numbers in question:

153 = 3 * 3 * 17

918 = 2 * 3 * 3 * 3 * 17

Circle anytime you see a number in both factorizations:

3 * 3 * 17

That's your GCF (Greatest Common Factor) of both numbers.