194 LearnersLast updated on May 26th, 2025
LCM of 24 and 56
LCM of any two numbers is the least common multiple of two numbers. In our daily lives, LCM is used for scheduling events and distributing items among us. In this topic, we will learn more about LCM of 24 and 56.
What is the LCM of 24 and 56
The common multiple of 24 and 56 is 168. Here, we will learn about the LCM of 2 numbers. Children learn about LCM at younger ages. Here, let’s discuss the methods used to find the LCM.
How to find the LCM of 24 and 56?
Out of many methods, the prime factorization method is widely used for its easy approach. Here, we will learn about other methods as well. A few commonly used methods are as follows -
- Listing Of Multiples
- Prime Factorization
- Division Method
LCM of 24 and 56 using listing multiple method
Listing multiples can be a tedious method for finding the LCM. Here, the listing of multiples for all these 2 numbers is noted -
- Multiples Of 24: 24, 48, 72, 96, 120, 144, 168
- Multiples of 56: 56, 112, 168, 224, 280, 336, 392,
- Then we can see that, out of 24 and 56, 168 is the smallest common number that is present in them. So we see that 168 is the LCM of 24 and 56.
LCM of 24 and 56 using prime Factorization Method
The product of the highest power of prime factors of 24 and 56 is the LCM of these numbers. So let us look at it step by step to understand it better.
Breaking the given numbers into their prime factors.
- Prime factorization of 24= 23 × 31
- Prime factorization of 56 = 2 x 2x 2x7
Multiplying the highest power of prime factors: 23 x31 x71
LCM of 24 and 56 is 168
LCM of 24 and 56 using the Division Method
In this method, we will be dividing the given numbers with the common prime factors until all numbers are reduced to 1. Let us look at this step by step and make it easy for the children to learn it.
Step 1: Arrange the numbers in a sequence, with divisors, on the left and numbers on the right sides.
Step 2: For finding the divisor, it is always the smallest common prime factor. Here, the smallest common prime factor is 2. Dividing 24 and 56 by 2. The result is 12 and 28.
Step 3: As 12 and 28 are divisible by 2, again the divisor is 2. Dividing 6 and 14 by 2. Now the result is 3 and 7.
Step 4: Continue dividing the numbers with the smallest prime number until all numbers are reduced to 1.
The divisors are 2, 2, 2, 3, 7 LCM of 24 and 56 is the product of divisors.
Hence, the LCM of (24 and 56) = 2 × 2 × 2 × 3 × 7 = 168
Common Mistakes and how to avoid them while finding the LCM of 24 and 56
There are some common mistakes that are made by children while solving a problem on LCM. Let us look at some of these mistakes and how we can help children to avoid these mistakes.
Mistake 1
Confusing factors and multiples.
Students used to confuse factors and multiples. To avoid confusion, students need to understand the concept of multiples and factors. Multiplies of a number are the product of the number with whole numbers, whereas factors of the number are the numbers which can evenly divide the number. For example, 1, 2, 3, 4, 6, and 12 are the factors of 12; whereas 12, 24, 36, 48, 60,… are the multiples of 12.
LCM of 24 and 56 Examples
Problem 1
Two bells toll at regular intervals, one bell tolls every 24 minutes, and the other tolls every 56 minutes, when will both bells toll together again?
By prime factorization:
24 = 23 × 3
56 = 23 × 7
Select the highest power of each prime:
2, 3, 7
Then multiply the highest power together:
LCM = 23 × 3 × 7 = 8 × 3 × 7 = 168
Explanation
The bells will toll together again in 168 minutes.
The LCM of 24 and 56 is 168
Problem 2
Find the LCM of 24, 56, and 36.
The LCM of 24, 56, and 36 by prime factorization method,
Prime factors of 24: 23 ×3
Prime factors of 36: 22 ×32
Prime factors of 56: 23 ×7
LCM (24, 36, 56) = 23 × 32 × 7 = 8 × 9 ×7 = 504
Explanation
Here, the smallest number (LCM) of 24, 56, and 36 is 504. That can be divided without leaving a remainder.
Problem 3
The product of two numbers is 1344. If their GCF is 8, what is their LCM?
Given GCF: 8
Product of numbers: 1344
Therefore, LCM x GCF = product of numbers
LCM = product / GCF
= 1344 / 8
Therefore, LCM is 168.
Explanation
The product of two numbers is 1344, and the GCD is 8. To calculate the LCM, divide the product by GCD. Then we get the LCM is 168.
LCM = 1344 8 = 168
FAQ on LCM of 24 and 56
1.What are the LCM and HCF of 24 and 56 by prime factorization method?
2.What is the LCM of 24 and 54?
3.What is the LCM of 24 and 56?
4.What is the ratio of 24 and 56?
5.How can children in United Kingdom use numbers in everyday life to understand LCM of 24 and 56?
6.What are some fun ways kids in United Kingdom can practice LCM of 24 and 56 with numbers?
7.What role do numbers and LCM of 24 and 56 play in helping children in United Kingdom develop problem-solving skills?
8.How can families in United Kingdom create number-rich environments to improve LCM of 24 and 56 skills?
Important Glossaries of LCM of 24 and 56
- Factor: A number that will divide two or more numbers, leaving no remainder. For 18 and 24 we have 6 as a common factor, it means both 18 and 24 can be divisible by 6.
- Prime Factorization: When a number can be represented as the factors of prime numbers, it is called prime factorization. The prime factorization of 18 for example is 2×3×3.
- Greatest Common Factor (GCF): GCF is the greatest factor that is common in the given numbers. For example, the GCF of 5, 10, and 15 is 5. Because the common factors of 5 and 10 are 1 and 5.
- Division Method: In the division method, the numbers are divided by the smallest common prime factor till the numbers are reduced to 1.
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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.
