LCM of 21 and 49
LCM of 21 and 49 is the smallest number among all common multiples of 21 and 49. The first few multiples of 21 and 49 are (21, 42, 63, 84, 105, 126, 147, . . . ) and (49, 98, 147, 196, 245, 294, 343, . . . ) respectively. There are 3 commonly used methods to find LCM of 21 and 49  by prime factorization, by listing multiples, and by division method.
1.  LCM of 21 and 49 
2.  List of Methods 
3.  Solved Examples 
4.  FAQs 
What is the LCM of 21 and 49?
Answer: LCM of 21 and 49 is 147.
Explanation:
The LCM of two nonzero integers, x(21) and y(49), is the smallest positive integer m(147) that is divisible by both x(21) and y(49) without any remainder.
Methods to Find LCM of 21 and 49
Let's look at the different methods for finding the LCM of 21 and 49.
 By Listing Multiples
 By Division Method
 By Prime Factorization Method
LCM of 21 and 49 by Listing Multiples
To calculate the LCM of 21 and 49 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 49 (49, 98, 147, 196, 245, 294, 343, . . . . )
 Step 2: The common multiples from the multiples of 21 and 49 are 147, 294, . . .
 Step 3: The smallest common multiple of 21 and 49 is 147.
∴ The least common multiple of 21 and 49 = 147.
LCM of 21 and 49 by Division Method
To calculate the LCM of 21 and 49 by the division method, we will divide the numbers(21, 49) by their prime factors (preferably common). The product of these divisors gives the LCM of 21 and 49.
 Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 21 and 49. Write this prime number(3) on the left of the given numbers(21 and 49), separated as per the ladder arrangement.
 Step 2: If any of the given numbers (21, 49) is a multiple of 3, divide it by 3 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 49 is the product of all prime numbers on the left, i.e. LCM(21, 49) by division method = 3 × 7 × 7 = 147.
LCM of 21 and 49 by Prime Factorization
Prime factorization of 21 and 49 is (3 × 7) = 3^{1} × 7^{1} and (7 × 7) = 7^{2} respectively. LCM of 21 and 49 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 3^{1} × 7^{2} = 147.
Hence, the LCM of 21 and 49 by prime factorization is 147.
☛ Also Check:
 LCM of 30, 36 and 40  360
 LCM of 11 and 22  22
 LCM of 4, 8 and 16  16
 LCM of 27 and 45  135
 LCM of 28 and 35  140
 LCM of 8 and 42  168
 LCM of 8 and 10  40
LCM of 21 and 49 Examples

Example 1: Find the smallest number that is divisible by 21 and 49 exactly.
Solution:
The smallest number that is divisible by 21 and 49 exactly is their LCM.
⇒ Multiples of 21 and 49: Multiples of 21 = 21, 42, 63, 84, 105, 126, 147, . . . .
 Multiples of 49 = 49, 98, 147, 196, 245, . . . .
Therefore, the LCM of 21 and 49 is 147.

Example 2: The product of two numbers is 1029. If their GCD is 7, what is their LCM?
Solution:
Given: GCD = 7
product of numbers = 1029
∵ LCM × GCD = product of numbers
⇒ LCM = Product/GCD = 1029/7
Therefore, the LCM is 147.
The probable combination for the given case is LCM(21, 49) = 147. 
Example 3: Verify the relationship between GCF and LCM of 21 and 49.
Solution:
The relation between GCF and LCM of 21 and 49 is given as,
LCM(21, 49) × GCF(21, 49) = Product of 21, 49
Prime factorization of 21 and 49 is given as, 21 = (3 × 7) = 3^{1} × 7^{1} and 49 = (7 × 7) = 7^{2}
LCM(21, 49) = 147
GCF(21, 49) = 7
LHS = LCM(21, 49) × GCF(21, 49) = 147 × 7 = 1029
RHS = Product of 21, 49 = 21 × 49 = 1029
⇒ LHS = RHS = 1029
Hence, verified.
FAQs on LCM of 21 and 49
What is the LCM of 21 and 49?
The LCM of 21 and 49 is 147. To find the LCM of 21 and 49, we need to find the multiples of 21 and 49 (multiples of 21 = 21, 42, 63, 84 . . . . 147; multiples of 49 = 49, 98, 147, 196) and choose the smallest multiple that is exactly divisible by 21 and 49, i.e., 147.
How to Find the LCM of 21 and 49 by Prime Factorization?
To find the LCM of 21 and 49 using prime factorization, we will find the prime factors, (21 = 3 × 7) and (49 = 7 × 7). LCM of 21 and 49 is the product of prime factors raised to their respective highest exponent among the numbers 21 and 49.
⇒ LCM of 21, 49 = 3^{1} × 7^{2} = 147.
What is the Relation Between GCF and LCM of 21, 49?
The following equation can be used to express the relation between GCF and LCM of 21 and 49, i.e. GCF × LCM = 21 × 49.
If the LCM of 49 and 21 is 147, Find its GCF.
LCM(49, 21) × GCF(49, 21) = 49 × 21
Since the LCM of 49 and 21 = 147
⇒ 147 × GCF(49, 21) = 1029
Therefore, the GCF = 1029/147 = 7.
Which of the following is the LCM of 21 and 49? 12, 147, 15, 3
The value of LCM of 21, 49 is the smallest common multiple of 21 and 49. The number satisfying the given condition is 147.
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