Practical Applications of LCM and GCF


The lowest common multiple or the LCM is defined as the smallest natural number that is divisible by a given set of integers. We use the list of natural numbers as the division of integers by zero remains undefined, and the numbers cannot equal 0. Thus, we use natural numbers instead of whole numbers. LCM is an acronym, and it stands for least common multiple. The LCM of two numbers, q, and v is represented by LCM (q, v).

Practical Applications of LCM

LCM method is used in the following fields

  • When we have to make computations regarding an event that is or will be repeating over and over, LCM is used.
  • LCM is used when we have to purchase or get several items so that we have enough.
  • To pinpoint if something will happen again at the same time.
  • In mathematical calculations. Suppose we have unlike fractions and we want to perform comparison, addition, or subtraction. As the denominators are not the same, hence we cannot compare, add or subtract the given fractions. In such a case, we have to find the LCM of the denominators and convert the fractions into like fractions and find the answer to our question.

Let us understand the applications with the help of examples.

1. Jack exercises every 10 days, and Jill exercises every 15 days. Jack and Jill both exercise today. How many days later will they exercise together?

Answer: As we are trying to find the earliest (least) time that the event of exercising (multiple) will occur at the same time (common) again, we have to use the LCM concept to figure out the answer. 

LCM of 10 and 15 is 30. Thus, Jack and Jill will exercise together after 30 days.

2. Add 7/10 and 2/15. 

Answer: As the denominators are different, i.e., 10 and 15, we have to use LCM to convert the unlike fractions into like fractions.

LCM of 10 and 15 is 30. If we multiply 10 by 3 and 15 by 2 we get 30. Thus, the fractions need to be multiplied by the same factor to convert them into like fractions.

7/10 * 3 = 21/30;

2/15 * 3 = 6/30;

On adding we get, 28/30. Simplifying this, we have 14/15


The greatest common factor or GCF is defined as the largest number that can divide a number into two or more equal parts. 

Practical Applications of GCF

  • Splitting things into smaller sections 
  • Used to figure out how many people to invite.
  • Arrange something into rows or groups

Example: Simon has two cloth pieces, one is 10 inches wide, and the other is 15 inches wide. He wants to cut both pieces into strips of equal width that are as wide as possible. How wide should the strips be?

Answer: We have to divide the strips into smaller pieces (factor) of 10 and 15 (common) while looking for the broadest possible strips (greatest). Thus, HCF has to be used. 

GCF of 10 and 15 is 5. Thus, each piece should be 5 inches wide.


LCM and GCF are important topics and can be learned well by joining an institution such as Cuemath. Children are provided with a holistic learning environment where they are encouraged to build solid concepts and have fun while studying. The certified tutors deliver impactful lectures and fun-filled lectures using resources such as worksheets, workbooks, puzzles, etc. A child is sure to master mathematics in no time under such care and precision.

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