LCM of 24 and 40
2026-02-28 01:29 Diff
https://brightchamps.com/en-us/math/numbers/lcm-of-24-and-40

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Last updated on August 5, 2025

LCM is a common multiple, the smallest value between the numbers 24 and 40. Did you know? We apply LCM unknowingly in everyday situations like setting alarms and to synchronize traffic lights and when making music.

What is the LCM of 24 and 40?

LCM of 24 and 40 Using Listing the Multiples

Step1: Write down the multiples of the numbers. Don’t stop too early.


  — Multiples of 24= 24,48,72,96,120,…


 — Multiples of 40 = 40,80,120,160,200


Step 2:  Find the smallest number common between the written multiples of 24 and 40


— The smallest common multiple is 120.


Thus, LCM (24,40) = 120
 

LCM of 24 and 40 Using Prime Factorization


Step1:  factorize the numbers into its prime factors 


24 = 2×2×2×3


40 = 2×2×2×5


Step2: find the highest powers of the factors of 24 and 40


Step3: Multiply the highest powers 


LCM(24,40) = 120

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LCM of 24 and 40 Using Division Method

  • Write the numbers 42,40 in a row 
  • Divide them by their common prime factors, if there is one
  • Carry forward the numbers that are left undivided by the previously chosen factor
  • Continue dividing until the remainder is ‘1’ 
  • Multiply the divisors to find the LCM
  • LCM (24,40) = 120
     

Common Mistakes and how to avoid them while finding the LCM of 24 and 40

Listed here are a few mistakes that one can commit when trying to find the LCM of the numbers 3 and 8. Try to avoid them. 
 

Problem 1

Verify the LCM-GCF relationship using the formula LCM(a,b)=a×b/GCF(a,b) for 18 and 24.

Okay, lets begin

GCF of 18 and 24 is 6.


Use the formula: LCM(18,24)=18×24/6=432/6=72
 

Explanation

LCM = 72, relationship verified. 
 

Well explained 👍

Problem 2

A running track is 24 meters long and 40 meters wide. What is the shortest length of a fence needed to enclose the track?

Okay, lets begin

The LCM of 24 and 40 is 120. 
 

Explanation

The smallest length that can be divided by both 24 and 40 can be divided by is 120. The shortest length of the fence is 120 meters. The LCM expresses the smallest common interval between the digits. 
 

Well explained 👍

Problem 3

The LCM of two numbers is 72. One of the numbers is 24. What is the other number?

Okay, lets begin

LCM = Product of the two numbers/GCF of the two numbers


The GCD of 24 and the unknown number is 6 (since LCM is 72).


Let the unknown number be x: 72=24×x/6


Solve: 72×6=24×x⇒x=432/24=18
 

Explanation

The other number is 18.
 

Well explained 👍

FAQ’s on LCM of 24 and 40

1.List the factors of 24 and 40.

 Numbers that are multiplied to reach 24 and 40 are called the factors of 24 and 40. 


Factors of 24 are 1,2,3,4,6,8,12,24


Factors of 40 are 1,2,4,5,8,10,20,40
 

2.What is the LCM of 40 and 40?

The LCM of the numbers is 40 itself. It is the smallest number that is divisible by itself. 

3.What is the LCM of 24 and 36?

72 is the smallest number that appears commonly on the lists of the numbers 24 and 36. 


LCM (24,36)= 72
 

4. What is the LCM of 24 and 30?

120 is the smallest number that appears commonly on the lists of the numbers 24 and 30. 


LCM (24,30)= 120
 

5. Is 12 a factor of 20?

No, 12 is not a factor of 20. When we divide 20 by 12, a remainder is left behind which makes it not a factor. 


20/12 = 1.667
 

Important glossaries for the LCM of 24 and 40

  • Multiple — product of a number and a natural integer 
  • Prime factor — number one gets after prime factorization any given number 
  • Prime factorization — the 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.