LCM and GCF
Posted by chanheeh on November 13, 2008
The least common multiple (LCM) of two numbers is the smallest number that is a multiple of both of the numbers. The greatest common factor (GCF) of two numbers is the greatest number that is a factor of both numbers. For example, LCM of 36 and 56 is 504 and GCF of 36 and 56 is 4.
We can find LCM and GCF very easily through prime factoring.
2 | 36 56
2 | 18 28
9 14
You have to stop at this point because there is no number that can divide both 9 and 14. And then 2*2 becomes the GCF of 36 and 56 and 2*2*9*14 is the LCM of two numbers.
Solve some practice problems.
1. Find the LCM and GCF of 64 and 120.
2. Find the LCM and GCF of 294 and 315.
Chanhee's Math Blog 
Jim Bogesvang said
Good work Chanhee! I like the algorithm you demonstrated. Perhaps even I have a chance at finding LCMs and GCFs ;^>.
Tatyana Malysh said
Actually it’s like to break it down to the prime numbers:
64=2×2×2×2×2×2 120=2×2×2×3×5
So, the part that is alike is 2×2×2=8 is GCF
And to make it the same we need to 2×2×2×2×2×2 × 3×5 = 960 is LCD
Leo said
Nice to read your article LCM and GCF…
for advanced ones, refer to Greatest Common Factor