227 LearnersLast updated on May 26th, 2025
LCM of 18,24 and 36
The LCM is a tool that is used to find the smallest common number between the given numbers. It helps us to coordinate schedules, organizing and solving math problems. Let’s learn more about the LCM of 18,24 and 36.
What is the LCM of 18,24 and 36?
The LCM of 18,24 and 36 is 72.
This answer can be found using different methods, they are explained below.
How to find the LCM of 18,24 and 36?
The LCM can be found by using the listing multiples method, the prime factorization method and the division method.
Listing multiples method
In the listing multiples methods, we list down the multiples of each of the numbers and find the smallest common multiple from the list.
In case of 18,24 and 36;
Multiples of-
18 = 18,36,54,72,...
24=24,48,72,...
36 = 36,72,...
LCM(18,24,36) = 72
Prime factorization method
Here, we break the numbers to their prime factors and then multiply the highest powers of each of the factors to get the LCM.
In case of 18,24 and 36;
Step 1: Prime factorize the numbers,
18 = 3×3×2
24= 2×2×2×3
36 = 2×2×3×3
Step 2: Find the highest powers
Highest powers of 2 = 23 , from 24
Highest powers of 3 = 32 , from 18 and 36
Step 3: LCM of the numbers is found by multiplying the highest powers
23×32 = 8×9 = 72
LCM(18,24,36) = 72
Division method
Follow the below instructions to find the LCM using the division method;
1.Write the numbers, 18,24,36 in a row
2.Start dividing the numbers with a prime factor that is divisible by at least one of the numbers
3.Continue to bring down the numbers if they are left undivided by the previously chosen factor
4.Conclude the division when the result of the last row is just ‘1’.
5.Multiply the divisors on the first column to get the LCM.
LCM(18,24,36) = 72
Common mistakes and how to avoid them in the LCM of 18,24 and 36
Listed below are a few common mistakes one may commit when learning to find the LCM of 18,24 and 36.
Mistake 1
Mistaking the highest power of prime factors
One may by accident, write down 22 instead of 23 from 24 and/or 33 instead of 32 from 18 and 36. This will affect the LCM result immensely.
LCM of 18,24 and 36 Examples
Problem 1
Find x. LCM(18,24,x)=72.
LCM of 18 and 24 = 72
The LCM of 18,24 and x should be a number that is divisible by all three numbers.
The LCM remains as 72.
Common factors of 72 = 1,2,3,6,12,18,24,36,72.
Explanation
the possible values for x will be any one of the listed factors. The LCM with all of the numbers above still remains as 72.
Problem 2
Verify if the LCM and the HCF of 18,24 and 36 are related.
Relationship between LCM and HCF -
LCM(a,b,c)×HCF(a,b,c) = a×b×c
LCM of 18,24,36 = 72
HCF of 18,24,36 = 6
Applying the formula
LCM(a,b,c)×HCF(a,b,c) = a×b×c
72×6 = 18×24×36
432=432
Explanation
The equation holds good, LHS = RHS.
Problem 3
Machine A beeps every 18 minutes, machine B every 24 minutes and machine C every 36 minutes. When will they next beep together?
The LCM of the numbers is 72.
Explanation
The smallest common time interval between the machines is 72 minutes, i.e., they will beep together in 72 minutes.
FAQs on the LCM of 18,24 and 36
1.What are the factors of 18,24 and 36?
2.What is the LCM of 8,16,24 and 36?
3.What is the LCM of 12,24 and 48?
4.Find the HCF of 16,24 and 36?
5.What is the LCM of 9,12 and 16?
6.How can children in United States use numbers in everyday life to understand LCM of 18,24 and 36 ?
7.What are some fun ways kids in United States can practice LCM of 18,24 and 36 with numbers?
8.What role do numbers and LCM of 18,24 and 36 play in helping children in United States develop problem-solving skills?
9.How can families in United States create number-rich environments to improve LCM of 18,24 and 36 skills?
Important glossaries for the LCM of 18,24 and 36
- Multiple: Product of any number and a natural integer
- Prime factor: number one gets after prime factorizing any given number
- Prime factorization: process of breaking the number into its prime factors
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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.
