178 LearnersLast updated on May 26th, 2025
LCM of 60 and 75
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
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!
Mistake 1
Duplicating or skipping a factor
A factor may be missed when we prime factorize a number. Writing the prime factorization of 75 may be written as 3×5×5×5 instead of 3×5×5 accidentally.
LCM of 60 and 75 Examples
Problem 1
Verify that the relationship between GCD and LCM holds true for 60 and 75: LCM(a, b)×GCD(a, b)=a×b
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.
Problem 2
What percentage of the product of 60 and 75 is their LCM?
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.
Problem 3
If the LCM of 60 and a missing number xxx is 300, what is xxx?
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.
Problem 4
Is 600 a common multiple of 60 and 75?
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.
FAQs on the LCM of 60 and 75
1. Find the GCF of 60 and 75 and list all the factors of the numbers.
2.Find the LCM of 60,75 and 90.
3.Find the LCM of 30,60 and 75?
4.Find the LCM of 50,60 and 75?
5. Find the LCM of 60,75 and 105?
6.How can children in India use numbers in everyday life to understand LCM of 60 and 75 ?
7.What are some fun ways kids in India can practice LCM of 60 and 75 with numbers?
8.What role do numbers and LCM of 60 and 75 play in helping children in India develop problem-solving skills?
9.How can families in India create number-rich environments to improve LCM of 60 and 75 skills?
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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About BrightChamps in India
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.
