What is the Difference Between GCF and LCM?

The main difference between GCF (Greatest Common Factor) and LCM (Least Common Multiple) lies in their definitions and purposes:

• GCF is the largest number that is a factor of two or more numbers. It represents the greatest common divisor among the given numbers, and it helps to simplify fractions or find the largest number that divides evenly into the given numbers.
• LCM is the smallest number that is a multiple of two or more numbers. It represents the smallest common multiple among the given numbers, and it helps to find the least common denominator when adding or subtracting fractions with different denominators.

In summary:

• GCF is the largest number that divides evenly into the given numbers.
• LCM is the smallest number that is a multiple of the given numbers.

To find the GCF and LCM of two or more numbers, you can use the prime factorization method, which involves finding the prime factors of each number and then identifying the greatest common factor or the least common multiple shared by the numbers.

Comparative Table: GCF vs LCM

The Greatest Common Factor (GCF) and the Least Common Multiple (LCM) are mathematical concepts related to factors and multiples of numbers. Here is a table highlighting the differences between GCF and LCM:

For example, to find the GCF and LCM of 24 and 36:

• GCF: Factors of 24 include 1, 2, 3, 4, 6, 8, 12, and 24. Factors of 36 include 1, 2, 3, 4, 6, 9, 12, 18, and 36. The greatest common factor is 12.
• LCM: Multiples of 24 include 24, 48, 72, 96, … and multiples of 36 include 36, 72, 108, 144, … The least common multiple is 72.