LCM of 15 and 21
LCM of 15 and 21 is the smallest number among all common multiples of 15 and 21. The first few multiples of 15 and 21 are (15, 30, 45, 60, 75, 90, . . . ) and (21, 42, 63, 84, 105, 126, . . . ) respectively. There are 3 commonly used methods to find LCM of 15 and 21  by listing multiples, by division method, and by prime factorization.
1.  LCM of 15 and 21 
2.  List of Methods 
3.  Solved Examples 
4.  FAQs 
What is the LCM of 15 and 21?
Answer: LCM of 15 and 21 is 105.
Explanation:
The LCM of two nonzero integers, x(15) and y(21), is the smallest positive integer m(105) that is divisible by both x(15) and y(21) without any remainder.
Methods to Find LCM of 15 and 21
Let's look at the different methods for finding the LCM of 15 and 21.
 By Division Method
 By Listing Multiples
 By Prime Factorization Method
LCM of 15 and 21 by Division Method
To calculate the LCM of 15 and 21 by the division method, we will divide the numbers(15, 21) by their prime factors (preferably common). The product of these divisors gives the LCM of 15 and 21.
 Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 15 and 21. Write this prime number(3) on the left of the given numbers(15 and 21), separated as per the ladder arrangement.
 Step 2: If any of the given numbers (15, 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 15 and 21 is the product of all prime numbers on the left, i.e. LCM(15, 21) by division method = 3 × 5 × 7 = 105.
LCM of 15 and 21 by Listing Multiples
To calculate the LCM of 15 and 21 by listing out the common multiples, we can follow the given below steps:
 Step 1: List a few multiples of 15 (15, 30, 45, 60, 75, 90, . . . ) and 21 (21, 42, 63, 84, 105, 126, . . . . )
 Step 2: The common multiples from the multiples of 15 and 21 are 105, 210, . . .
 Step 3: The smallest common multiple of 15 and 21 is 105.
∴ The least common multiple of 15 and 21 = 105.
LCM of 15 and 21 by Prime Factorization
Prime factorization of 15 and 21 is (3 × 5) = 3^{1} × 5^{1} and (3 × 7) = 3^{1} × 7^{1} respectively. LCM of 15 and 21 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 3^{1} × 5^{1} × 7^{1} = 105.
Hence, the LCM of 15 and 21 by prime factorization is 105.
☛ Also Check:
 LCM of 36 and 42  252
 LCM of 36 and 40  360
 LCM of 35 and 70  70
 LCM of 35 and 60  420
 LCM of 35 and 55  385
 LCM of 35 and 49  245
 LCM of 35 and 45  315
LCM of 15 and 21 Examples

Example 1: The product of two numbers is 315. If their GCD is 3, what is their LCM?
Solution:
Given: GCD = 3
product of numbers = 315
∵ LCM × GCD = product of numbers
⇒ LCM = Product/GCD = 315/3
Therefore, the LCM is 105.
The probable combination for the given case is LCM(15, 21) = 105. 
Example 2: The GCD and LCM of two numbers are 3 and 105 respectively. If one number is 15, find the other number.
Solution:
Let the other number be p.
∵ GCD × LCM = 15 × p
⇒ p = (GCD × LCM)/15
⇒ p = (3 × 105)/15
⇒ p = 21
Therefore, the other number is 21. 
Example 3: Verify the relationship between GCF and LCM of 15 and 21.
Solution:
The relation between GCF and LCM of 15 and 21 is given as,
LCM(15, 21) × GCF(15, 21) = Product of 15, 21
Prime factorization of 15 and 21 is given as, 15 = (3 × 5) = 3^{1} × 5^{1} and 21 = (3 × 7) = 3^{1} × 7^{1}
LCM(15, 21) = 105
GCF(15, 21) = 3
LHS = LCM(15, 21) × GCF(15, 21) = 105 × 3 = 315
RHS = Product of 15, 21 = 15 × 21 = 315
⇒ LHS = RHS = 315
Hence, verified.
FAQs on LCM of 15 and 21
What is the LCM of 15 and 21?
The LCM of 15 and 21 is 105. To find the least common multiple of 15 and 21, we need to find the multiples of 15 and 21 (multiples of 15 = 15, 30, 45, 60 . . . . 105; multiples of 21 = 21, 42, 63, 84 . . . . 105) and choose the smallest multiple that is exactly divisible by 15 and 21, i.e., 105.
How to Find the LCM of 15 and 21 by Prime Factorization?
To find the LCM of 15 and 21 using prime factorization, we will find the prime factors, (15 = 3 × 5) and (21 = 3 × 7). LCM of 15 and 21 is the product of prime factors raised to their respective highest exponent among the numbers 15 and 21.
⇒ LCM of 15, 21 = 3^{1} × 5^{1} × 7^{1} = 105.
If the LCM of 21 and 15 is 105, Find its GCF.
LCM(21, 15) × GCF(21, 15) = 21 × 15
Since the LCM of 21 and 15 = 105
⇒ 105 × GCF(21, 15) = 315
Therefore, the GCF = 315/105 = 3.
Which of the following is the LCM of 15 and 21? 2, 105, 12, 24
The value of LCM of 15, 21 is the smallest common multiple of 15 and 21. The number satisfying the given condition is 105.
What is the Relation Between GCF and LCM of 15, 21?
The following equation can be used to express the relation between GCF and LCM of 15 and 21, i.e. GCF × LCM = 15 × 21.
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