LCM of 21 and 56
LCM of 21 and 56 is the smallest number among all common multiples of 21 and 56. The first few multiples of 21 and 56 are (21, 42, 63, 84, 105, . . . ) and (56, 112, 168, 224, . . . ) respectively. There are 3 commonly used methods to find LCM of 21 and 56  by listing multiples, by prime factorization, and by division method.
1.  LCM of 21 and 56 
2.  List of Methods 
3.  Solved Examples 
4.  FAQs 
What is the LCM of 21 and 56?
Answer: LCM of 21 and 56 is 168.
Explanation:
The LCM of two nonzero integers, x(21) and y(56), is the smallest positive integer m(168) that is divisible by both x(21) and y(56) without any remainder.
Methods to Find LCM of 21 and 56
Let's look at the different methods for finding the LCM of 21 and 56.
 By Listing Multiples
 By Prime Factorization Method
 By Division Method
LCM of 21 and 56 by Listing Multiples
To calculate the LCM of 21 and 56 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, . . . ) and 56 (56, 112, 168, 224, . . . . )
 Step 2: The common multiples from the multiples of 21 and 56 are 168, 336, . . .
 Step 3: The smallest common multiple of 21 and 56 is 168.
∴ The least common multiple of 21 and 56 = 168.
LCM of 21 and 56 by Prime Factorization
Prime factorization of 21 and 56 is (3 × 7) = 3^{1} × 7^{1} and (2 × 2 × 2 × 7) = 2^{3} × 7^{1} respectively. LCM of 21 and 56 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 56 by prime factorization is 168.
LCM of 21 and 56 by Division Method
To calculate the LCM of 21 and 56 by the division method, we will divide the numbers(21, 56) by their prime factors (preferably common). The product of these divisors gives the LCM of 21 and 56.
 Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 21 and 56. Write this prime number(2) on the left of the given numbers(21 and 56), separated as per the ladder arrangement.
 Step 2: If any of the given numbers (21, 56) 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 56 is the product of all prime numbers on the left, i.e. LCM(21, 56) by division method = 2 × 2 × 2 × 3 × 7 = 168.
☛ Also Check:
 LCM of 11 and 12  132
 LCM of 3 and 13  39
 LCM of 3 and 5  15
 LCM of 64 and 96  192
 LCM of 30 and 35  210
 LCM of 13 and 20  260
 LCM of 45 and 75  225
LCM of 21 and 56 Examples

Example 1: The GCD and LCM of two numbers are 7 and 168 respectively. If one number is 21, find the other number.
Solution:
Let the other number be y.
∵ GCD × LCM = 21 × y
⇒ y = (GCD × LCM)/21
⇒ y = (7 × 168)/21
⇒ y = 56
Therefore, the other number is 56. 
Example 2: The product of two numbers is 1176. If their GCD is 7, what is their LCM?
Solution:
Given: GCD = 7
product of numbers = 1176
∵ LCM × GCD = product of numbers
⇒ LCM = Product/GCD = 1176/7
Therefore, the LCM is 168.
The probable combination for the given case is LCM(21, 56) = 168. 
Example 3: Find the smallest number that is divisible by 21 and 56 exactly.
Solution:
The smallest number that is divisible by 21 and 56 exactly is their LCM.
⇒ Multiples of 21 and 56: Multiples of 21 = 21, 42, 63, 84, 105, 126, 147, 168, . . . .
 Multiples of 56 = 56, 112, 168, 224, 280, 336, 392, . . . .
Therefore, the LCM of 21 and 56 is 168.
FAQs on LCM of 21 and 56
What is the LCM of 21 and 56?
The LCM of 21 and 56 is 168. To find the LCM (least common multiple) of 21 and 56, we need to find the multiples of 21 and 56 (multiples of 21 = 21, 42, 63, 84 . . . . 168; multiples of 56 = 56, 112, 168, 224) and choose the smallest multiple that is exactly divisible by 21 and 56, i.e., 168.
Which of the following is the LCM of 21 and 56? 21, 12, 168, 36
The value of LCM of 21, 56 is the smallest common multiple of 21 and 56. The number satisfying the given condition is 168.
If the LCM of 56 and 21 is 168, Find its GCF.
LCM(56, 21) × GCF(56, 21) = 56 × 21
Since the LCM of 56 and 21 = 168
⇒ 168 × GCF(56, 21) = 1176
Therefore, the greatest common factor (GCF) = 1176/168 = 7.
What is the Relation Between GCF and LCM of 21, 56?
The following equation can be used to express the relation between GCF and LCM of 21 and 56, i.e. GCF × LCM = 21 × 56.
What is the Least Perfect Square Divisible by 21 and 56?
The least number divisible by 21 and 56 = LCM(21, 56)
LCM of 21 and 56 = 2 × 2 × 2 × 3 × 7 [Incomplete pair(s): 2, 3, 7]
⇒ Least perfect square divisible by each 21 and 56 = LCM(21, 56) × 2 × 3 × 7 = 7056 [Square root of 7056 = √7056 = ±84]
Therefore, 7056 is the required number.
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