Being able to determine the greatest common factor (GCF) and least common multiple (LCM) of a set of numbers is a very useful skill. For those who are unsure of what GCF and LCM are:
GCF (Greatest Common Factor): The highest number that divides exactly into two or more numbers.
LCM (Least Common Multiple): The smallest number that is a multiple of two or more numbers.
To find either the LCM or the GCF of two or more numbers, you start the same way: begin with prime factorization of all numbers. A useful trick to keeping things organized and easily understood would be to put your factors into a nice, neat “grid” consisting of rows and columns (this is shown in the example below). You then compare and contrast what you need.
To find GCF, multiply all prime factors that are shared between the numbers including repeating common factors.
To find LCM, multiply all factors for each number including repeated factors.
This can best be seen through example.
Consider two numbers: 136 and 84
First, we need to perform prime factorization on both numbers and construct a “grid”:
We then look for shared factors in order to find GCF. As we can see from our grid, the only common factor between 136 and 84 is 2 and a copy of 2; therefore, the GCF is 4.
To find the LCM, we look at all factors. We can see that the factors are 2, 3, 7, and 17. We also have to include repeated factors and then multiply them all together:
2x2x2x3x7x17=2856
Therefore the LCM is 2856.
It may be helpful to understand how I got these values when the factors are lined up in a more organized way:
136: 2 2 2 17
84: 2 2 3 7
———————-
2×2 = 4 got GCF
2x2x2x3x7x17 = 2856 for LCM
This article was written for you by Troy, one of the tutors with SchoolTutoring Academy.