LCM of 120 and 150
2026-02-28 11:27 Diff
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Last updated on August 5, 2025

LCM is the smallest and a common multiple of the numbers 120 and 150. We often apply the LCM to solve problems that have in them fractions, percentages, time intervals and others. Below, we explain how we find the LCM of 120 and 150.

What is the LCM of 120 and 150?

LCM of 120 and 150 Using Listing the Multiples

Step 1: List multiples of the numbers; 


120–120,240,360,480,600,…


150– 150,300,450,600,…


Step 2: Find the smallest common number 


LCM(120,150) = 600 
 

LCM of 120 and 150 Using Prime Factorization

Step 1: Prime factorize the numbers 


120 = 2×2×2×3×5


150= 2×3×5×5


Step 2: Multiply highest powers 


23×3×52 = 600 


LCM(120,150) = 600 
 

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LCM of 120 and 150 Using Division Method

  • Write the numbers in a row 
  • Divide them by their common prime factors 
  • Carry forward the numbers that are not divided by the previously chosen number
  • Continue dividing until the remainder is ‘1’ 
  • Multiply the divisors to find the LCM — 2×2×2×3×5×5 = 600
  • LCM(120,150) = 600 
     

Common mistakes to avoid while finding the LCM of 120 and 150

Listed here are a few mistakes that are frequently made when trying to find the LCM. 
 

Problem 1

Two machines A and B complete a cycle in 120 and 150 minutes, respectively. After how many minutes will both machines complete their cycle together again?

Okay, lets begin

The LCM(120, 150) = 600 minutes. 
 

Explanation

 Both machines will complete a cycle together in 600 minutes.
 

Well explained 👍

Problem 2

The LCM of two numbers is 36 and the sum is 21. Find the numbers.

Okay, lets begin

LCM(a, b) = 36 


a+b= 21


We know that, LCM(a, b)×HCF(a, b) =a×b 


Let us assume that the numbers a and b are 8 and 10, 


8+10 = 18, it is not equal to the sum given


Let us assume that the numbers a and b are 12 and 30,


30+12= 42, which is equal to the sum given


Product of 12 and 30; 


30 ×12= 360


LCM(a, b)×HCF(a, b) =a×b 


LCM (30,12)×HCF(30,12) =30×12 


LCM of 30,12; 


Prime factorization of 12  = 2×2×3


Prime factorization of 30 =  5×2×3


LCM(30,12) = 60


HCF of 30,12; 


Factors of 30 = 1,2,3,5,6,10,15,30 


Factors of 12 = 1,2,3,4,6,12


HCF(30,12) = 6


60×6 =30×12 


360 =360 
 

Explanation

 We, by assuming that a and b are 12 and 30 respectively and verifying the same against the formula figures that the assumption is right and a=12,b=30. 
 

Well explained 👍

Problem 3

If 120 items represent 20% of a total, and 150 items represent 25% of another total, what is the least common multiple of the totals?

Okay, lets begin

20% = 120 


Total = 120/ 0.2 = 600


25% = 150 


Total = 150/0.25 = 600 
 

Explanation

Thus, the LCM of the totals is 600.
 

Well explained 👍

FAQs on the LCM of 120 and 150

1.What is the HCF of 120 and 150?

Factors of 120–1,2,3,4,5,6,8,10,12,15,20,24,30,40,60,120 


Factors of 150–1,2,3,5,6,10,15,25,30,50,75,150 


HCF(120,150) = 30 
 

2.What is the LCM of 125 and 150?

LCM(125,150) = 750. 750 is the smallest common multiple number of the numbers 125 and 150.
 

3.What is the LCM of 100,150 and 120.

The smallest number and a common multiple of the numbers 100,150 and 120 is their LCM. LCM of 100,150 and 120 is 600. 
 

4.What is the LCM of 45,120 and 150?

1800 is the LCM of 45,120 and 150. It is the smallest number and a common multiple of the numbers 45,12 and 150. 
 

5.What is the LCM of 150 and 225?

LCM of 150 and 225 = 450. 450 is the smallest multiple of 150 and 225. 

Important glossaries for LCM of 120 and 150

  • Multiple: product of a number and integer  
  • Prime Factor: a number whose factors are itself and 1 
  • Prime Factorization: breaking a large 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.