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254 LearnersLast updated on November 29th, 2024
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
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?
Explanation
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?
Explanation
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?
Explanation
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.
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
: She loves to read number jokes and games.
