LCM of 3 and 21
LCM of 3 and 21 is the smallest number among all common multiples of 3 and 21. The first few multiples of 3 and 21 are (3, 6, 9, 12, 15, 18, 21, . . . ) and (21, 42, 63, 84, 105, . . . ) respectively. There are 3 commonly used methods to find LCM of 3 and 21  by prime factorization, by division method, and by listing multiples.
1.  LCM of 3 and 21 
2.  List of Methods 
3.  Solved Examples 
4.  FAQs 
What is the LCM of 3 and 21?
Answer: LCM of 3 and 21 is 21.
Explanation:
The LCM of two nonzero integers, x(3) and y(21), is the smallest positive integer m(21) that is divisible by both x(3) and y(21) without any remainder.
Methods to Find LCM of 3 and 21
The methods to find the LCM of 3 and 21 are explained below.
 By Prime Factorization Method
 By Listing Multiples
 By Division Method
LCM of 3 and 21 by Prime Factorization
Prime factorization of 3 and 21 is (3) = 3^{1} and (3 × 7) = 3^{1} × 7^{1} respectively. LCM of 3 and 21 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 3^{1} × 7^{1} = 21.
Hence, the LCM of 3 and 21 by prime factorization is 21.
LCM of 3 and 21 by Listing Multiples
To calculate the LCM of 3 and 21 by listing out the common multiples, we can follow the given below steps:
 Step 1: List a few multiples of 3 (3, 6, 9, 12, 15, 18, 21, . . . ) and 21 (21, 42, 63, 84, 105, . . . . )
 Step 2: The common multiples from the multiples of 3 and 21 are 21, 42, . . .
 Step 3: The smallest common multiple of 3 and 21 is 21.
∴ The least common multiple of 3 and 21 = 21.
LCM of 3 and 21 by Division Method
To calculate the LCM of 3 and 21 by the division method, we will divide the numbers(3, 21) by their prime factors (preferably common). The product of these divisors gives the LCM of 3 and 21.
 Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 3 and 21. Write this prime number(3) on the left of the given numbers(3 and 21), separated as per the ladder arrangement.
 Step 2: If any of the given numbers (3, 21) 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 3 and 21 is the product of all prime numbers on the left, i.e. LCM(3, 21) by division method = 3 × 7 = 21.
☛ Also Check:
 LCM of 520 and 468  4680
 LCM of 3 and 9  9
 LCM of 9 and 10  90
 LCM of 25 and 45  225
 LCM of 25 and 100  100
 LCM of 8, 12, 15 and 20  120
 LCM of 13 and 39  39
LCM of 3 and 21 Examples

Example 1: The product of two numbers is 63. If their GCD is 3, what is their LCM?
Solution:
Given: GCD = 3
product of numbers = 63
∵ LCM × GCD = product of numbers
⇒ LCM = Product/GCD = 63/3
Therefore, the LCM is 21.
The probable combination for the given case is LCM(3, 21) = 21. 
Example 2: Find the smallest number that is divisible by 3 and 21 exactly.
Solution:
The smallest number that is divisible by 3 and 21 exactly is their LCM.
⇒ Multiples of 3 and 21: Multiples of 3 = 3, 6, 9, 12, 15, 18, 21, . . . .
 Multiples of 21 = 21, 42, 63, 84, 105, 126, 147, . . . .
Therefore, the LCM of 3 and 21 is 21.

Example 3: Verify the relationship between GCF and LCM of 3 and 21.
Solution:
The relation between GCF and LCM of 3 and 21 is given as,
LCM(3, 21) × GCF(3, 21) = Product of 3, 21
Prime factorization of 3 and 21 is given as, 3 = (3) = 3^{1} and 21 = (3 × 7) = 3^{1} × 7^{1}
LCM(3, 21) = 21
GCF(3, 21) = 3
LHS = LCM(3, 21) × GCF(3, 21) = 21 × 3 = 63
RHS = Product of 3, 21 = 3 × 21 = 63
⇒ LHS = RHS = 63
Hence, verified.
FAQs on LCM of 3 and 21
What is the LCM of 3 and 21?
The LCM of 3 and 21 is 21. To find the least common multiple (LCM) of 3 and 21, we need to find the multiples of 3 and 21 (multiples of 3 = 3, 6, 9, 12 . . . . 21; multiples of 21 = 21, 42, 63, 84) and choose the smallest multiple that is exactly divisible by 3 and 21, i.e., 21.
What is the Relation Between GCF and LCM of 3, 21?
The following equation can be used to express the relation between GCF and LCM of 3 and 21, i.e. GCF × LCM = 3 × 21.
If the LCM of 21 and 3 is 21, Find its GCF.
LCM(21, 3) × GCF(21, 3) = 21 × 3
Since the LCM of 21 and 3 = 21
⇒ 21 × GCF(21, 3) = 63
Therefore, the greatest common factor = 63/21 = 3.
How to Find the LCM of 3 and 21 by Prime Factorization?
To find the LCM of 3 and 21 using prime factorization, we will find the prime factors, (3 = 3) and (21 = 3 × 7). LCM of 3 and 21 is the product of prime factors raised to their respective highest exponent among the numbers 3 and 21.
⇒ LCM of 3, 21 = 3^{1} × 7^{1} = 21.
Which of the following is the LCM of 3 and 21? 12, 24, 21, 42
The value of LCM of 3, 21 is the smallest common multiple of 3 and 21. The number satisfying the given condition is 21.
visual curriculum