LCM of 3,4 and 5
2026-02-28 12:45 Diff
https://brightchamps.com/en-us/math/numbers/lcm-of-3-4-and-5

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Last updated on August 5, 2025

The smallest positive integer that divides the numbers with no numbers left behind is the LCM of 3,4 and 5. Did you know? We apply LCM unknowingly in everyday situations like setting alarms and to synchronize traffic lights and when making music. In this article, let’s now learn to find LCMs of 3,4 and 5.

What is LCM of 3,4 and 5

We can find the LCM using listing multiples method, prime factorization method and the long division method. These methods are explained here, apply a method that fits your understanding well. 
 

LCM of 3,4 and 5 using listing multiples method

Step 1: List the multiples of each of the numbers; 


3 =3,6,9,12,15,18,21,24,27,30,33,36,39,42,45,…60


4= 4,8,12,16,20,…60


5= 5,10,15,20,…60


Step 2:Find the smallest number in both the lists 


LCM (3,4,5) = 60

LCM of 3,4 and 5 using prime factorization method

Step 1: Prime factorize the numbers 


3 = 3


4 = 2×2


5 = 5 


Step 2: find highest powers


Step 3: Multiply the highest powers of the numbers


LCM(3,4,5) = 60

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LCM of 3,4 and 5 using division method

  • Write the numbers in a row 
  • Divide them with a common prime factor
  • Carry forward numbers that are left undivided 
  • Continue dividing until the remainder is ‘1’ 
  • Multiply the divisors to find the LCM
  • LCM (3,4,5) = 60 
     

Common mistakes and how to avoid them in LCM of 3,4 and 5

Listed here are a few mistakes children may make when trying to find the LCM due to confusion or due to unclear understanding. Be mindful, understand, learn and avoid!
 

Problem 1

A number is divisible by both 3 and 4 but not divisible by 5. If the LCM of 3, 4, and another number is 60, what is the missing number?

Okay, lets begin

Since the number is divisible by both 3 and 4, its LCM with these numbers must be divisible by their LCM (which is 12).

However, it should not include a factor of 5.


The number that satisfies this condition is 12, since:


LCM(3, 4, 12) = 60.
 

Explanation

The missing number is 12.
 

Well explained 👍

Problem 2

If n=LCM(3,4,5), find the number of divisors of n.

Okay, lets begin

 First, find the LCM(3, 4, 5) = 60 (already solved).


Now, find the number of divisors of 60. The prime factorization of 60 is:


60=22×3×5


The number of divisors of a number is given by the formula:


Number of divisors=(e1+1)(e2+1)…(ek+1)


where e1, e2, …, ek are the exponents in the prime factorization.


For 60:


Number of divisors=(2+1)(1+1)(1+1)=3×2×2=12

Explanation

 The number of divisors of 60 is 12.

Well explained 👍

Problem 3

If the GCF of two numbers is 1 and their LCM is 60, what can you say about the numbers if one of them is 4?

Okay, lets begin

Let the two numbers be 4 and x. We are given:


GCF(4,x)=1 and LCM(4,x)=60


Since GCF(4, x) = 1, x must not share any prime factors with 4 (which has the prime factorization 22).


Thus, x must be divisible by 3 and 5 (since 60=22×3×5, and we already accounted for the 22in 4).

Therefore,

x=15x = 15x=15.
 

Explanation

The other number is 15.
 

Well explained 👍

FAQs on the LCM of 3,4 and 5

1.What is the LCM of 2,3 and 4?

Multiples of 2 = 2,4,6,8,10,12,…

 
Multiples of 3 = 3,6,9,12,…


Multiples of 4 = 4,8,12,…


LCM(2,3,4) = 12 
 

2.What are the factors of 3,4, and 5?

— 3 = (1,3) 


— 4 =  (1,2,4) 


— 5 = (1,5) 


GCF(3,4,5) = 1
 

3. What is the LCM of 4 and 7?

 4 and 7 are co-prime, the LCM is just the product, i.e., 28. 

4.What is the GCF of 17 and 19?

— Factors of 17 = 1,17


— Factors of 19 = 1,19 


GCF (17,19) = 1 

Important glossaries for LCM of 3,4 and 5

  • Multiple: the result after multiplication of a number and an integer. To explain, 5×5 =25; 25 is a multiple of 5. 
  • Prime Factor: A number with only two factors, 1 and the number. For example,7, its factors are only 1 and 7 and the number when divided by any other integer will leave a remainder behind. 
  • Prime Factorization: breaking a number down into its prime factors. For example, 60 is written as the product of 2×2×3×5. 
     

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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.