- GCF stands for "Greatest Common Factor". To find the GCF of the given numbers, list all the factors of the given numbers and then find the largest common factor.
- LCM stands for "Least Common Multiple". To find the LCM of the given numbers, list the multiples of the given numbers until you find the smallest common multiple.
Example 1: Find the GCF of 36 and 54.
Factors of 36 :
Factors of 54:
The greatest common factor is 18.
Example 2: Find the GCF of 49 and 63.
Factors of 49:
Factors of 63:
The greatest common factor is 7.
Example 3: Find the LCM of 12 and 9.
Multiples of 12: 12, 24, 36, 48, 60
Multiples of 9: 9, 18, 27, 36, 45
The least common multiple is 36.
Example 4: Find the LCM of 24 and 36.
Multiples of 24: 24, 48, 72, 96
Multiples of 36: 36, 72, 108
The least common multiple is 72.
- GCF is the largest common factor of all the possible factors of the given numbers.
- LCM is the smallest common multiple of the given numbers.
- Being able to recognize the GCF and LCM of given numbers comes in handy when performing operations with fractions.
- LCD stands for the least common denominator.
- LCD of the given fractions is the LCM of the denominators of the given fractions.
- Example of the use of GCF in daily life: distributing items equally into groups without any leftovers
- Examples of the use of LCM in daily life: to find out when the bikers riding a bike in a loop at different speeds will meet, or a train running at different speeds will cross.
- LCM should not be confused with GCF.