159 LearnersLast updated on May 26th, 2025
LCM of 21 and 24
The meaning of least common factor (LCM) is to find the smallest number that divides any two integers evenly. LCM is used mainly in fractions to find a common number for both the integers. We use LCM for solving problems, lining up cycles or even synchronizing of events, also to schedule tasks in everyday life.
What is the LCM of 21 and 24?
We use LCM of 21 and 24 to find the smallest number that divides both the numbers equally. The smallest positive number is the number that divides both numbers equally, is 168 without leaving any remainder. LCM is used mainly in fractions to find a common number for both the integers.
How to find the LCM of 21 and 24?
The LCM of 21 and 24 can be found by the following methods like division method, listing multiples, prime factorization.
LCM of 21 and 24 using Division method:
In division method, we divide both the numbers, we begin with dividing side by side the smallest number. We continue dividing until we get a common number that divides both the numbers equally. It makes it easier for the children to focus on prime factors and identify them.
- 2 divides 24 and not 21
- 3 divides 24 and 21
- 12 divides 24 and not 21
- 7 divides 21 and not 24.
Now multiply the divisors : 2×3×4×7=168 which is the LCM.
LCM of 24 and 21 using Listing multiples:
Step 1: Start by listing multiples of both the numbers separately:
Multiples of 21 are 21,42,63,84,105,126,147,168…..
Multiples of 24 are 24,48,72,96120,144,168…..
Step 2: The least common factor from the list is 168. Therefore, the LCM of 24 and 21 is 168.
LCM of 24 and 21 using Prime factorization:
We part both the numbers unto factors:
Factor of 24: 23×3
Factors of 21: 3×7
Take the powers of both the numbers and multiply together:
LCM=23x3x7=168.
Common Mistakes and How to Avoid Them in LCM of 24 and 21
While solving problems based on the LCM of 24 and 21, children fail to understand few concepts, to give an idea of the mistakes, given below are a few mistakes and solutions of how to avoid them:
Mistake 1
Stopping the division method way too soon.
Students sometimes stop dividing very soon, when they are not able to divide both the numbers with the same number. For example, we can divide14 by 2, but 15 isn't divisible by 2. To continue the dividing method until all the factors are found. The students should continue dividing until they find the common number that divides both the integers.
LCM of 24 and 21 Examples
Problem 1
Is 504 a common multiple of 24 and 21?
504/ 24=21
504/21=24
Explanation
As both divisions leave no remainder, 504 is a common multiple of 24 and 21.
Problem 2
Simplify the fraction 24/21 using the GCD of the numerator and denominator.
the simplified fraction is 8/7.
Explanation
GCD (24,21) =3
Divide both numerator and denominator by 3:
24/3 ÷ 21/3=8/7
Therefore, the simplified fraction is 8/7.
Problem 3
List the first 5 multiples of 24 and 21. Identify the LCM from these lists.
Multiples of 24: 24,48,72,96,120,144,168,…
Multiples of 21: 21,42,63,84,105,126,147,168,….
Explanation
LCM of 24 and 21 = 168
Problem 4
Find the value of X, if LCM(24,X)=168.
Answer: X=21.
Explanation
Using the formula :
LCM(a, b) x GCD(a, b)=a × b
LCM(24,X)=168
GCD(24,X)=unknown
As the product of numbers should be equal to 168, so X=21.
LCM(24,21)=168.
X=21.
Problem 5
Find the simplified form of 24/21.
GCD(24,21)=3
24/ 21 = 24÷3 / 21 ÷3 = 8/7
Explanation
simplified form of 24/21 is 8/7
FAQ’s on LCM of 24 and 21
1. What is the number that can be divided by 21 and 24?
2.There are how many factors in 4800?
3.Write the LCM of 21,24, and 18?
4.What is the GCF of 240 and 360?
5.What is the GCF of 300 by factor tree method?
6.How can children in Qatar use numbers in everyday life to understand LCM of 21 and 24?
7.What are some fun ways kids in Qatar can practice LCM of 21 and 24 with numbers?
8.What role do numbers and LCM of 21 and 24 play in helping children in Qatar develop problem-solving skills?
9.How can families in Qatar create number-rich environments to improve LCM of 21 and 24 skills?
Important glossaries on the LCM of 24 and 21
- Prime Factor: A natural number or whole number which has factors that are 1 and itself. For Example, 3 is a prime number.
- Prime Factorization: The process of breaking down a number into its prime factors is called Prime Factorization. For example, the factorization of 14 is 2×7.
- Co-prime numbers: numbers which has the only positive divisor of them both as 1. For example, 6 and 7.
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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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