LCM of 60 and 75
2026-02-28 12:56 Diff
https://brightchamps.com/en-us/math/numbers/lcm-of-60-and-75

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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 60 and 75. 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 60 and 75.

What is LCM of 60 and 75

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 60 and 75 using listing multiples method

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


60 = 60,120,180,240,300,… 


75= 75,150,225,300,…


Step 2: Find the smallest number in both the lists 


LCM (60,75) = 300 
 

LCM of 60 and 75 using prime factorization method

Step 1:Prime factorize the numbers

 
60 = 2×2×3×5


75 = 3×5×5 


Step 2:find highest powers


22,3 and 52 


Step 3: Multiply the highest powers of the numbers


22×3×52 = 300 


LCM(60,75) = 300 
 

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LCM of 60 and 75 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 (60,75) = 300 
     

Common mistakes and how to avoid them while finding the LCM of 60 and 75

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

Verify that the relationship between GCD and LCM holds true for 60 and 75: LCM(a, b)×GCD(a, b)=a×b

Okay, lets begin

GCD(60, 75) = 15

LCM(60, 75) = 300

LCM (60,75)×GCD(60,75) = 300×15 = 4500

60×75 = 4500
 

Explanation

The formula holds because the product of the LCM and GCD equals the product of the original numbers.
 

Well explained 👍

Problem 2

What percentage of the product of 60 and 75 is their LCM?

Okay, lets begin

Product of 60 and 75 =  60 × 75 = 4500


LCM = 300


Percentage = 300/4500×100 =  6.67%
 

Explanation

 The LCM is 6.67% of the product of the two numbers.

Well explained 👍

Problem 3

If the LCM of 60 and a missing number xxx is 300, what is xxx?

Okay, lets begin

LCM(60,x) = 300


Prime factorization of 60 = 2² × 3 × 5


Since 300 = 2² × 3 × 5²,

the missing number x must provide the extra factor of 5.


Thus, x=75
 

Explanation

The missing number x is the number that would provide the required factors to make the LCM 300.

Well explained 👍

Problem 4

Is 600 a common multiple of 60 and 75?

Okay, lets begin

600/60 = 10


600/75 = 8
 

Explanation

Since 600 is divisible by both 60 and 75, it is a common multiple. However, it is not the least common multiple, as the LCM is 300.
 

Well explained 👍

FAQs on the LCM of 60 and 75

1. Find the GCF of 60 and 75 and list all the factors of the numbers.

Factors of;


60–1,2,3,4,5,6,10,12,15,20,30,60


75–1,3,5,15,25,75


GCF(60,75) = 15 

2.Find the LCM of 60,75 and 90.

Prime factorization of the numbers 60,75 and 90; 


60 = 2×2×3×5


75 = 3×5×5


90= 3×3×2×5 


LCM (60,75,90) = 900
 

3.Find the LCM of 30,60 and 75?

Prime factorization of the numbers 30,60 and75;


30 =2×3×5


60 = 2×2×3×5


75 = 3×5×5


LCM (30,60,75) = 300
 

4.Find the LCM of 50,60 and 75?

Prime factorization of the numbers; 


50 = 2×5×5


60 = 2×2×3×5


75 = 3×5×5


LCM (50,30,60) = 300
 

5. Find the LCM of 60,75 and 105?

Write down the multiples of the numbers 


60 = 60,120,180,240,30,…2100


75 = 75,150,225,300,….2100

105 = 105,210,315,420,…2100


LCM (60,75,105) = 2100 
 

Important glossaries for LCM of 60 and 75

  • Multiple: the result after multiplication of a number and an integer. To explain, 75×5 =375; 375 is a multiple of 75. 
  • 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.