281 LearnersLast updated on May 26th, 2025
LCM of 24 and 30
The Least common multiple (LCM) is the smallest number that is divisible by the numbers 24 and 30. LCM helps to solve problems with fractions and scenarios like scheduling or aligning repeating cycle of events.
What is the LCM of 24 and 30?
The LCM of 24 and 30 is the smallest positive integer, a multiple of both numbers. By finding the LCM, we can simplify the arithmetic operations like addition and subtraction with fractions to equate the denominators.
How to find the LCM of 24 and 30 ?
There are various methods to find the LCM, Listing method, prime factorization method and division method are explained below;
LCM of 24 and 30 using the Listing multiples method
To ascertain the LCM, list the multiples of the integers until a common multiple is found.
Step 1: Writedown the multiples of each number:
Multiples of 24 = 24,48,…,120,…
Multiples of 30 = 30,…,120,…
Step 2. Ascertain the smallest multiple from the listed multiples of 24 and 30.
The LCM (The Least common multiple) of 24 and 30 is 24. I.e., 120 is divisible by 24 and 30 with no reminder.
LCM of 24 and 30 using the Prime Factorization
This method involves finding the prime factors of each number and then multiplying the highest power of the prime factors to get the LCM.
Step1: Find the prime factors of the numbers:
Prime factorization of 24 = 2×2×2×3
Prime factorization of 30 = 2×3×5
Step 2: Take the highest power of each prime factor:
— 2,2,2,3,5
Step 3: Multiply the ascertained factors to get the LCM:
LCM (8,12) = 2×2×2×3×5 = 120
LCM of 24 and 30 using the Division Method
The Division Method involves 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: Divide the row of numbers by a prime number that is evenly divisible into at least one of the given 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.,
2×2×2×3×5 = 120
LCM (24,30) = 120
Common Mistakes and how to avoid them in LCM of 24 and 30
Listed below are a few commonly made mistakes while attempting to ascertain the LCM of 24 and 30, make a note while practicing.
Mistake 1
Confusing between LCM and HCF of the numbers 24 and 30
It is common for one to be confused between the HCF (Highest common factor) and LCM (least common multiple).
LCM is the smallest number divisible by 24 and 30 while, the largest number that divides them both is the HCF.
A simple trick to remember is that the HCF is going to be a relatively smaller number, it deals with divisors.
For LCM, however, the number will be at least as large as the largest of the two numbers.
In the given case, the HCF is 6, and the LCM is 120.
LCM of 24 and 30 Examples
Problem 1
Trains Y and X arrive every 8 minutes and 12 minutes at the station at the same time. In how long will they arrive together again?
The LCM of 24 and 30 = 120
Explanation
The smallest common multiple is ascertained between the numbers to ascertain the next arrival of the trains at the same time, which is in 120 minutes.
Problem 2
In a factory, machine A finishes a cycle every 24 minutes, machine B finishes a cycle in 30 minutes. Using the LCM formula, ascertain when will they complete a cycle simultaneously?
We use the formula;
LCM(a, b) = a×b/HCF(a, b) where, a=24, b=30
HCF of 24 and 30;
Factors of 24 = 1,2,3,4,6,8,12,24
Factors of 30 = 1,2,3,5,6,10,15,30
HCF (24,30)= 6
Applying the ascertained HCF in the formula;
LCM(a, b) = a×b/HCF(a, b)
LCM(24,30) = 24×30/6 = 120
LCM(24,30) = 120
Explanation
Machines A and B will complete their cycle together every 120 minutes.
Problem 3
Student A finishes his work in 24 minutes and student B finishes his work in 30 minutes. If A and B start working together, after how long will they complete the task?
To begin, calculate the work rates of student A and B;
Student A = 1/24
Student B = 1/30
Combined work rate;
1/24+1/30
To add the fractions, equate the denominators by finding their LCM
Prime factorization of 24 = 2×2×2×3
Prime factorization of 30 = 2×3×5
LCM of 24, 30 = 120
1/24 ×5/5 = 5/120
1/30×4/4 = 4/120
Combined work rate = 5/120+4/120 = 9/120 = 13.33 minutes
Explanation
Students A and B will complete their task in approximately 13.33 minutes if they work together.
FAQ’s on LCM of 24 and 30
1.What is the HCF of 24 and 30?
2. List the factors of 24 and 30.
3.What is the LCM of 25 and 30?
4.What is the LCM of 20 and 30?
5. List the prime factors of 30.
6.How can children in Qatar use numbers in everyday life to understand LCM of 24 and 30?
7.What are some fun ways kids in Qatar can practice LCM of 24 and 30 with numbers?
8.What role do numbers and LCM of 24 and 30 play in helping children in Qatar develop problem-solving skills?
9.How can families in Qatar create number-rich environments to improve LCM of 24 and 30 skills?
Important glossaries for LCM of 24 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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