LCM of 21 and 30
LCM of 21 and 30 is the smallest number among all common multiples of 21 and 30. The first few multiples of 21 and 30 are (21, 42, 63, 84, 105, . . . ) and (30, 60, 90, 120, . . . ) respectively. There are 3 commonly used methods to find LCM of 21 and 30  by division method, by listing multiples, and by prime factorization.
1.  LCM of 21 and 30 
2.  List of Methods 
3.  Solved Examples 
4.  FAQs 
What is the LCM of 21 and 30?
Answer: LCM of 21 and 30 is 210.
Explanation:
The LCM of two nonzero integers, x(21) and y(30), is the smallest positive integer m(210) that is divisible by both x(21) and y(30) without any remainder.
Methods to Find LCM of 21 and 30
The methods to find the LCM of 21 and 30 are explained below.
 By Division Method
 By Prime Factorization Method
 By Listing Multiples
LCM of 21 and 30 by Division Method
To calculate the LCM of 21 and 30 by the division method, we will divide the numbers(21, 30) by their prime factors (preferably common). The product of these divisors gives the LCM of 21 and 30.
 Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 21 and 30. Write this prime number(2) on the left of the given numbers(21 and 30), separated as per the ladder arrangement.
 Step 2: If any of the given numbers (21, 30) 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 30 is the product of all prime numbers on the left, i.e. LCM(21, 30) by division method = 2 × 3 × 5 × 7 = 210.
LCM of 21 and 30 by Prime Factorization
Prime factorization of 21 and 30 is (3 × 7) = 3^{1} × 7^{1} and (2 × 3 × 5) = 2^{1} × 3^{1} × 5^{1} respectively. LCM of 21 and 30 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2^{1} × 3^{1} × 5^{1} × 7^{1} = 210.
Hence, the LCM of 21 and 30 by prime factorization is 210.
LCM of 21 and 30 by Listing Multiples
To calculate the LCM of 21 and 30 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 30 (30, 60, 90, 120, . . . . )
 Step 2: The common multiples from the multiples of 21 and 30 are 210, 420, . . .
 Step 3: The smallest common multiple of 21 and 30 is 210.
∴ The least common multiple of 21 and 30 = 210.
☛ Also Check:
 LCM of 25 and 45  225
 LCM of 2, 4 and 8  8
 LCM of 378, 180 and 420  3780
 LCM of 45 and 120  360
 LCM of 45 and 72  360
 LCM of 9 and 30  90
 LCM of 12 and 30  60
LCM of 21 and 30 Examples

Example 1: Verify the relationship between GCF and LCM of 21 and 30.
Solution:
The relation between GCF and LCM of 21 and 30 is given as,
LCM(21, 30) × GCF(21, 30) = Product of 21, 30
Prime factorization of 21 and 30 is given as, 21 = (3 × 7) = 3^{1} × 7^{1} and 30 = (2 × 3 × 5) = 2^{1} × 3^{1} × 5^{1}
LCM(21, 30) = 210
GCF(21, 30) = 3
LHS = LCM(21, 30) × GCF(21, 30) = 210 × 3 = 630
RHS = Product of 21, 30 = 21 × 30 = 630
⇒ LHS = RHS = 630
Hence, verified. 
Example 2: Find the smallest number that is divisible by 21 and 30 exactly.
Solution:
The smallest number that is divisible by 21 and 30 exactly is their LCM.
⇒ Multiples of 21 and 30: Multiples of 21 = 21, 42, 63, 84, 105, 126, 147, 168, 189, 210, . . . .
 Multiples of 30 = 30, 60, 90, 120, 150, 180, 210, . . . .
Therefore, the LCM of 21 and 30 is 210.

Example 3: The product of two numbers is 630. If their GCD is 3, what is their LCM?
Solution:
Given: GCD = 3
product of numbers = 630
∵ LCM × GCD = product of numbers
⇒ LCM = Product/GCD = 630/3
Therefore, the LCM is 210.
The probable combination for the given case is LCM(21, 30) = 210.
FAQs on LCM of 21 and 30
What is the LCM of 21 and 30?
The LCM of 21 and 30 is 210. To find the LCM of 21 and 30, we need to find the multiples of 21 and 30 (multiples of 21 = 21, 42, 63, 84 . . . . 210; multiples of 30 = 30, 60, 90, 120 . . . . 210) and choose the smallest multiple that is exactly divisible by 21 and 30, i.e., 210.
If the LCM of 30 and 21 is 210, Find its GCF.
LCM(30, 21) × GCF(30, 21) = 30 × 21
Since the LCM of 30 and 21 = 210
⇒ 210 × GCF(30, 21) = 630
Therefore, the greatest common factor (GCF) = 630/210 = 3.
Which of the following is the LCM of 21 and 30? 210, 5, 15, 16
The value of LCM of 21, 30 is the smallest common multiple of 21 and 30. The number satisfying the given condition is 210.
What are the Methods to Find LCM of 21 and 30?
The commonly used methods to find the LCM of 21 and 30 are:
 Prime Factorization Method
 Listing Multiples
 Division Method
What is the Least Perfect Square Divisible by 21 and 30?
The least number divisible by 21 and 30 = LCM(21, 30)
LCM of 21 and 30 = 2 × 3 × 5 × 7 [Incomplete pair(s): 2, 3, 5, 7]
⇒ Least perfect square divisible by each 21 and 30 = LCM(21, 30) × 2 × 3 × 5 × 7 = 44100 [Square root of 44100 = √44100 = ±210]
Therefore, 44100 is the required number.