178 LearnersLast updated on May 26th, 2025
LCM of 25 and 30
The LCM helps to solve problems with fractions and scenarios like scheduling or aligning repeating cycle of events also in something as common as setting an alarm. In this article, we will learn more about the LCM of 25and 30.
What is the LCM of 25and 30?
The LCM of 25and 30 is the smallest positive integer, a multiple of both numbers. By finding the LCM, we can simplify the arithmetic operations with fractions to equate the denominators.
How to find the LCM of 25and 30 ?
There are various methods to find the LCM, Listing method, prime factorization method and division method are explained below;
LCM of 25 and 30 using the Listing multiples method
The LCM of 25and 30 can be found using the following steps;\
Step 1: Write down the multiples of each number:
Multiples of 25= 25,50,75,100,125,150,…
Multiples of 30 = 30,60,90,120,150,…
Step 2:Ascertain the smallest multiple from the listed multiples of 25and 30. The least common multiple of the numbers 25and 30 is 150
LCM of 25 and 30 using the Listing multiples method
The LCM of 25and 30 can be found using the following steps;
Step 1:Write down the multiples of each number:
Multiples of 25= 25,50,75,100,125,150,…
Multiples of 30 = 30,60,90,120,150,…
Step 2: A scertain the smallest multiple from the listed multiples of 25and 30. The least common multiple of the numbers 25and 30 is 150
LCM of 25 and 30 using the Prime Factorization
The prime factors of each number are written, and then the highest power of the prime factors is multiplied to get the LCM.
Step 1: Find the prime factors of the numbers:
Prime factorization of 25 = 5×5
Prime factorization of 30 = 2×5×3
Step 2: Multiply the highest power of each factor ascertained to get the LCM:
LCM (15,30) = 150
LCM of 25and 30 using the Division Method
The Division Method involves simultaneously dividing the numbers by their prime factors and multiplying the divisors to get the LCM.
Step 1: Write down the numbers in a row;
Step 2: A prime integer that is evenly divisible into at least one of the provided numbers should be used to divide the row of numbers.
Step 3: Continue dividing the numbers until the last row of the results is ‘1’ and bring down the numbers not divisible by the previously chosen prime number.
Step 4: The LCM of the numbers is the product of the prime numbers in the first column, i.e,
LCM (25,30) = 150
Common Mistakes and how to avoid them in LCM of 25 and 30
Listed below are a few commonly made mistakes while attempting to ascertain the LCM of 25 and 30, make a note while practicing.
Mistake 1
Stopping at ‘a’ common multiple
Students often overlook the least common multiple and assume that a common multiple is the LCM of the given digits. Emphasis lies on the word ‘least’ while trying to find the LCM.
LCM of 25 and 30, Examples
Problem 1
Find the LCM of 5x2 and 30x3
Prime factorize the given expressions;
5x2 = 5×x2
30x3= 2×3×5×x3
Explanation
We take the highest power of all the factors in the expression, the LCM of 5x2 and 30x3 = 30x3.
Problem 2
Prove → LCM(a,b)×HCF(a,b)=a×b in the case of 25 and 30.
LCM of 25,30;
Prime factorization of 25= 5×5
Prime factorization of 30 = 2×5×3
LCM(25,30) = 150
HCF of 25,30;
Factors of 25= 1,5,25
Factors of 30 = 1,2,3,5,6,10,15,30
HCF(25,30) = 5
Now applying the formula;
LCM(a,b)×HCF(a,b)=a×b
LCM(25,30)×HCF(25,30)=25×30
150×5=25×30
750=750
Explanation
LHS = RHS, the verification is hence justified. The property applied; The product of HCF and LCM of a and b is equal to the product of a and b themselves.
Problem 3
Simplify — 25/30
Find the HCF, to make the simplification simpler, the HCF is a divisor of both the numbers.
HCF of 25,30;
Factors of 25= 1,5,25
Factors of 30 = 1,2,3,5,6,10,15,30
HCF(25,30) = 5
Now, we simplify the fraction;
(25/5)/(30/5) = 5/6 =0.833
Explanation
We simplified the fraction easily using the HCF of the numbers.
FAQ’s on LCM of 25 and 30
1.What is the LCM of 24 and 30?
2.What is the HCF of 25and 30?
3.What is the LCM of 10,25and 30?
4.What is the LCM of 15,24 and 30?
5.What is the LCM of 12,25and 30?
6.How can children in United Kingdom use numbers in everyday life to understand LCM of 25 and 30?
7.What are some fun ways kids in United Kingdom can practice LCM of 25 and 30 with numbers?
8.What role do numbers and LCM of 25 and 30 play in helping children in United Kingdom develop problem-solving skills?
9.How can families in United Kingdom create number-rich environments to improve LCM of 25 and 30 skills?
Important glossaries for LCM of 25 and 30
- Multiple: A number and any integer multiplied.
- Prime Factor: A natural number (other than 1) that has factors that are one and itself.
- Prime Factorization: The process of breaking down a number into its prime factors is called Prime Factorization.
- Co-prime numbers: When the only positive integer that is a divisor of them both is 1, a number is co-prime.
- Relatively Prime Numbers: Numbers that have no common factors other than 1.
- Fraction: A representation of a part of a whole.
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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
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