245 LearnersLast updated on August 29, 2025
LCM (Least Common Multiple)
LCM stands for lowest common multiple. The smallest multiple which is common among two or more numbers is the LCM of the number. LCM is used to predict and schedule events.
Importance of LCM in Mathematics
Methods to Find LCM
There are various methods to find the LCM of any two numbers. The few common methods are listing the multiples, prime factorization, and division methods.
Method 1: Listing the multiples
In this method, the multiples of the given numbers are listed to find the smallest common multiple.
For example,
LCM of 10 and 20
Multiples of 10 – 10, 20, 30, 40, …
Multiples of 20 – 20, 40, 60, 80, …
Therefore, the LCM (10, 20) = 20.
LCM of 10, 20, and 30
Multiples of 10 – 10, 20, 30, 40, …
Multiples of 20 – 20, 40, 60, 80, ….
Multiples of 30 – 30, 60, 90, ……
Therefore, the LCM (10, 20, 30) = 60.
Method 2: Prime factorization method
The product of the highest power of all the prime factors of the given numbers is the LCM.
For example,
LCM of 10 and 20
Prime factorization of 10 = 2 × 5
Prime factorization of 20 = 22 × 5
LCM(10, 20) = 22 × 5 = 4 × 5 = 20.
LCM of 10, 20, and 30
Prime factorization of 10 = 2 × 5
Prime factorization of 20 = 22 × 5
Prime factorization of 30 = 2 × 3 × 5
LCM(10, 20) = 22 × 3 × 5 = 4 × 3 × 5 = 60.
Method 3: Division method
In the division method, the given number is divided by its smallest common prime factor till we get 1. The LCM is the product of the divisors.
For example,
LCM of 10 and 20
LCM (10, 20) = 2 × 2 × 5 = 20
LCM of 10, 20, and 30
LCM (10, 20, 30) = 2 × 2 × 3 × 5 = 60
Real-world application of LCM
LCM is used in daily life for different applications to predict, and schedule recurring events etc. In this section, let’s learn about the real-world application of LCM.
Event planning: When the events recur in a fixed interval, we use LCM to predict the next events or when they occur simultaneously.
Buses running on schedules: To schedule the timing of buses, we use LCM of the intervals to find the time when the buses come.
To synchronize events: When multiple processes occur at different intervals, we identify the common time by finding the LCM.
Common Mistakes and How to Avoid Them in LCM
LCM is used in different branches of math, and students tend to make errors when finding LCM. Mistakes are common among students and in this section, we will explore common mistakes.
Mistake 1
Misunderstanding the concept of LCM and GCF
Confusing LCM and GCF is a common error made by students, to avoid it students should be aware of the concept of LCM and GCF. LCM is about multiples and GCF is about the factors.
Mistake 2
Errors in the division method
While using the division method, the number should be divided only by the prime factors. And the process should be continued until all the numbers become 1.
Mistake 3
Confusing with the relationship between LCM and GCF.
Students tend to be confused with the relation between the LCM and GCF. The relationship between LCM and GCF is that the product of the number is equal to the product of LCM and GCF.
Mistake 4
Confusing that the product of two numbers is the LCM
Students think that the product of two numbers is the LCM, whereas it is not true in all cases. It only works for the co-primes.
Mistake 5
Errors in listing multiples
When listing multiples to find the LCM, students may list multiples incorrectly. So try to double-check the multiples and verify whether it's correct or not.
Tips and Tricks to Master LCM
As LCM is used in many branches of math, it is important to master LCM. In this section, let’s learn a few tips and tricks to master LCM.
Understanding the concept of LCM:
Learning the basic concept of LCM makes it easy for students to master LCM.
LCM is the smallest common multiple among two or more numbers.
Understanding the relationship between LCM and GCF:
The product of two numbers is the product of LCM and GCF.
Therefore, LCM(a, b) = Product of a and b / GCF (a, b).
LCM of prime numbers:
LCM of any prime number is the product of the prime numbers.
For example, LCM of 5 and 11 is 5 ×11 = 55
Solved Examples of LCM
Problem 1
If a bus and train come in an interval of 5 and 10 minutes respectively. Find when both the train and bus come together.
Both the bus and train come together every 10 minutes.
Explanation
To predict the event, we find the LCM of the intervals.
Here we find the LCM of 5 and 10
Multiples of 5 are 5, 10, 15, 20, 30, …
Multiples of 10 are 10, 20, 30, ….
LCM (5, 10) = 10
Problem 2
Sam has swimming class every 5 days and drawing classes every 3 days. On which day will he have both classes together?
Sam will have both the classes together on every 15th day
Explanation
To find when he has both the class, we find the LCM of 5 and 3.
As both 5 and 3 are prime numbers, LCM (5, 3) is 5 × 3 = 15.
Problem 3
If the LCM and product of two numbers are 175 and 875. Find the GCF of the numbers.
The GCF of two numbers is 5
Explanation
The GCF is calculated using the equation,
LCM × GCF = Product of the two numbers
Given, LCM = 175
Product of the numbers = 875
GCF = Product of two numbers / LCM
= 875 / 175
= 5
FAQs on LCM
1.What is the LCM of 24 and 36?
2.What is the LCM of 12 and 6?
3.List the methods to calculate LCM.
4.What is the LCM of 5 and 11?
5.How can children in United States use numbers in everyday life to understand LCM (Least Common Multiple)?
6.What are some fun ways kids in United States can practice LCM (Least Common Multiple) with numbers?
7.What role do numbers and LCM (Least Common Multiple) play in helping children in United States develop problem-solving skills?
8.How can families in United States create number-rich environments to improve LCM (Least Common Multiple) skills?
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Hiralee Lalitkumar Makwana
About the Author
Hiralee Lalitkumar Makwana has almost two years of teaching experience. She is a number ninja as she loves numbers. Her interest in numbers can be seen in the way she cracks math puzzles and hidden patterns.
Fun Fact
: She loves to read number jokes and games.
