LCM of 21 and 24
LCM of 21 and 24 is the smallest number among all common multiples of 21 and 24. The first few multiples of 21 and 24 are (21, 42, 63, 84, 105, 126, 147, . . . ) and (24, 48, 72, 96, 120, 144, . . . ) respectively. There are 3 commonly used methods to find LCM of 21 and 24  by division method, by listing multiples, and by prime factorization.
1.  LCM of 21 and 24 
2.  List of Methods 
3.  Solved Examples 
4.  FAQs 
What is the LCM of 21 and 24?
Answer: LCM of 21 and 24 is 168.
Explanation:
The LCM of two nonzero integers, x(21) and y(24), is the smallest positive integer m(168) that is divisible by both x(21) and y(24) without any remainder.
Methods to Find LCM of 21 and 24
Let's look at the different methods for finding the LCM of 21 and 24.
 By Listing Multiples
 By Division Method
 By Prime Factorization Method
LCM of 21 and 24 by Listing Multiples
To calculate the LCM of 21 and 24 by listing out the common multiples, we can follow the given below steps:
 Step 1: List a few multiples of 21 (21, 42, 63, 84, 105, 126, 147, . . . ) and 24 (24, 48, 72, 96, 120, 144, . . . . )
 Step 2: The common multiples from the multiples of 21 and 24 are 168, 336, . . .
 Step 3: The smallest common multiple of 21 and 24 is 168.
∴ The least common multiple of 21 and 24 = 168.
LCM of 21 and 24 by Division Method
To calculate the LCM of 21 and 24 by the division method, we will divide the numbers(21, 24) by their prime factors (preferably common). The product of these divisors gives the LCM of 21 and 24.
 Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 21 and 24. Write this prime number(2) on the left of the given numbers(21 and 24), separated as per the ladder arrangement.
 Step 2: If any of the given numbers (21, 24) is a multiple of 2, divide it by 2 and write the quotient below it. Bring down any number that is not divisible by the prime number.
 Step 3: Continue the steps until only 1s are left in the last row.
The LCM of 21 and 24 is the product of all prime numbers on the left, i.e. LCM(21, 24) by division method = 2 × 2 × 2 × 3 × 7 = 168.
LCM of 21 and 24 by Prime Factorization
Prime factorization of 21 and 24 is (3 × 7) = 3^{1} × 7^{1} and (2 × 2 × 2 × 3) = 2^{3} × 3^{1} respectively. LCM of 21 and 24 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2^{3} × 3^{1} × 7^{1} = 168.
Hence, the LCM of 21 and 24 by prime factorization is 168.
☛ Also Check:
 LCM of 25, 40 and 60  600
 LCM of 12 and 13  156
 LCM of 5 and 15  15
 LCM of 24 and 48  48
 LCM of 7, 11, 21 and 22  462
 LCM of 16 and 24  48
 LCM of 11 and 22  22
LCM of 21 and 24 Examples

Example 1: Find the smallest number that is divisible by 21 and 24 exactly.
Solution:
The smallest number that is divisible by 21 and 24 exactly is their LCM.
⇒ Multiples of 21 and 24: Multiples of 21 = 21, 42, 63, 84, 105, 126, 147, 168, . . . .
 Multiples of 24 = 24, 48, 72, 96, 120, 144, 168, . . . .
Therefore, the LCM of 21 and 24 is 168.

Example 2: Verify the relationship between GCF and LCM of 21 and 24.
Solution:
The relation between GCF and LCM of 21 and 24 is given as,
LCM(21, 24) × GCF(21, 24) = Product of 21, 24
Prime factorization of 21 and 24 is given as, 21 = (3 × 7) = 3^{1} × 7^{1} and 24 = (2 × 2 × 2 × 3) = 2^{3} × 3^{1}
LCM(21, 24) = 168
GCF(21, 24) = 3
LHS = LCM(21, 24) × GCF(21, 24) = 168 × 3 = 504
RHS = Product of 21, 24 = 21 × 24 = 504
⇒ LHS = RHS = 504
Hence, verified. 
Example 3: The product of two numbers is 504. If their GCD is 3, what is their LCM?
Solution:
Given: GCD = 3
product of numbers = 504
∵ LCM × GCD = product of numbers
⇒ LCM = Product/GCD = 504/3
Therefore, the LCM is 168.
The probable combination for the given case is LCM(21, 24) = 168.
FAQs on LCM of 21 and 24
What is the LCM of 21 and 24?
The LCM of 21 and 24 is 168. To find the LCM (least common multiple) of 21 and 24, we need to find the multiples of 21 and 24 (multiples of 21 = 21, 42, 63, 84 . . . . 168; multiples of 24 = 24, 48, 72, 96 . . . . 168) and choose the smallest multiple that is exactly divisible by 21 and 24, i.e., 168.
How to Find the LCM of 21 and 24 by Prime Factorization?
To find the LCM of 21 and 24 using prime factorization, we will find the prime factors, (21 = 3 × 7) and (24 = 2 × 2 × 2 × 3). LCM of 21 and 24 is the product of prime factors raised to their respective highest exponent among the numbers 21 and 24.
⇒ LCM of 21, 24 = 2^{3} × 3^{1} × 7^{1} = 168.
If the LCM of 24 and 21 is 168, Find its GCF.
LCM(24, 21) × GCF(24, 21) = 24 × 21
Since the LCM of 24 and 21 = 168
⇒ 168 × GCF(24, 21) = 504
Therefore, the greatest common factor = 504/168 = 3.
What is the Relation Between GCF and LCM of 21, 24?
The following equation can be used to express the relation between GCF and LCM of 21 and 24, i.e. GCF × LCM = 21 × 24.
What are the Methods to Find LCM of 21 and 24?
The commonly used methods to find the LCM of 21 and 24 are:
 Listing Multiples
 Prime Factorization Method
 Division Method
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