140 LearnersLast updated on May 26th, 2025
LCM of 30 and 75
The smallest positive integer that divides the numbers with no numbers left behind is the LCM of 30 and 75. Did you know? We apply LCM unknowingly in everyday situations like setting alarms and to synchronise traffic lights and when making music. In this article, let’s now learn to find LCMs of 30 and 75.
What is LCM of 30 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 30 and 75 using listing multiples method
Step1: List the multiples of each of the numbers;
30 = 30,60,90,120,150,180,…
75= 75,150,225,300,…
Step 2: Find the smallest number in both the lists
LCM (30,75) = 150
LCM of 30 and 75 using prime factorization method
Step 1: Prime factorize the numbers
30 = 2×3×5
75 = 3×5×5
Step 2:find highest powers.
Step 3:Multiply the highest powers of the numbers
LCM(30,75) = 150
LCM of 30 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 (30,75) = 150
Common mistakes and how to avoid them in LCM of 30 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 30 and 75 Examples
Problem 1
Prove that the LCM of two numbers a and b, where GCF(a, b)=d, can be written as LCM(a, b)=a×b LCM(a, b)=a×b​ using a=30 and b=75.
a = 30, b=75
d=GCF(30,75)=15
By the formula: LCM(30,75)= 30×75/GCF(30,75)
30×75/15=150
The LCM matches the direct calculation using prime factorization.
Explanation
This problem uses the property that the product of two numbers divided by their GCF gives the LCM, providing a mathematical verification.
Problem 2
If the GCF of two numbers is 15 and one of the numbers is 30, use the formula to find the LCM of these two numbers.
Formula: LCM(a, b)=a×b/GCF(a, b)
Given a=30, GCF(a, b)=15 and let b=75
LCM(30,75)=30×75/15=2250/15=150
Explanation
Using the relationship between the GCF and LCM, we can quickly compute the LCM of the two numbers.
Problem 3
John exercises every 30 days and Sarah exercises every 75 days. If they both exercised today, in how many days will they exercise together again?
The number of days when they will both exercise together again is the LCM of 30 and 75.
LCM(30,75)=150
So, they will both exercise together again in 150 days.
Explanation
The LCM of their exercise intervals gives the earliest day they will coincide again.
FAQs on the LCM of 30 and 75
1.What is the GCF of 30 and 75?
2.Find the LCM of 25 and 75.
3. What is the LCM of 40 and 75?
4.What is the LCM of 50 and 75?
5.What is the LCM of 30,45 and 75?
6.How can children in United States use numbers in everyday life to understand LCM of 30 and 75?
7.What are some fun ways kids in United States can practice LCM of 30 and 75 with numbers?
8.What role do numbers and LCM of 30 and 75 play in helping children in United States develop problem-solving skills?
9.How can families in United States create number-rich environments to improve LCM of 30 and 75 skills?
Important glossaries for LCM of 30 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, 30 is written as the product of 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.
