LCM of 15 and 20
LCM of 15 and 20 is the smallest number among all common multiples of 15 and 20. The first few multiples of 15 and 20 are (15, 30, 45, 60, 75, 90, 105, . . . ) and (20, 40, 60, 80, 100, 120, . . . ) respectively. There are 3 commonly used methods to find LCM of 15 and 20  by division method, by prime factorization, and by listing multiples.
1.  LCM of 15 and 20 
2.  List of Methods 
3.  Solved Examples 
4.  FAQs 
What is the LCM of 15 and 20?
Answer: LCM of 15 and 20 is 60.
Explanation:
The LCM of two nonzero integers, x(15) and y(20), is the smallest positive integer m(60) that is divisible by both x(15) and y(20) without any remainder.
Methods to Find LCM of 15 and 20
The methods to find the LCM of 15 and 20 are explained below.
 By Prime Factorization Method
 By Division Method
 By Listing Multiples
LCM of 15 and 20 by Prime Factorization
Prime factorization of 15 and 20 is (3 × 5) = 3^{1} × 5^{1} and (2 × 2 × 5) = 2^{2} × 5^{1} respectively. LCM of 15 and 20 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2^{2} × 3^{1} × 5^{1} = 60.
Hence, the LCM of 15 and 20 by prime factorization is 60.
LCM of 15 and 20 by Division Method
To calculate the LCM of 15 and 20 by the division method, we will divide the numbers(15, 20) by their prime factors (preferably common). The product of these divisors gives the LCM of 15 and 20.
 Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 15 and 20. Write this prime number(2) on the left of the given numbers(15 and 20), separated as per the ladder arrangement.
 Step 2: If any of the given numbers (15, 20) 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 15 and 20 is the product of all prime numbers on the left, i.e. LCM(15, 20) by division method = 2 × 2 × 3 × 5 = 60.
LCM of 15 and 20 by Listing Multiples
To calculate the LCM of 15 and 20 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, 105, . . . ) and 20 (20, 40, 60, 80, 100, 120, . . . . )
 Step 2: The common multiples from the multiples of 15 and 20 are 60, 120, . . .
 Step 3: The smallest common multiple of 15 and 20 is 60.
∴ The least common multiple of 15 and 20 = 60.
☛ Also Check:
 LCM of 36 and 72  72
 LCM of 36 and 64  576
 LCM of 36 and 63  252
 LCM of 36 and 60  180
 LCM of 36 and 54  108
 LCM of 36 and 48  144
 LCM of 36 and 45  180
LCM of 15 and 20 Examples

Example 1: Find the smallest number that is divisible by 15 and 20 exactly.
Solution:
The smallest number that is divisible by 15 and 20 exactly is their LCM.
⇒ Multiples of 15 and 20: Multiples of 15 = 15, 30, 45, 60, 75, 90, 105, . . . .
 Multiples of 20 = 20, 40, 60, 80, 100, 120, 140, . . . .
Therefore, the LCM of 15 and 20 is 60.

Example 2: The GCD and LCM of two numbers are 5 and 60 respectively. If one number is 15, find the other number.
Solution:
Let the other number be a.
∵ GCD × LCM = 15 × a
⇒ a = (GCD × LCM)/15
⇒ a = (5 × 60)/15
⇒ a = 20
Therefore, the other number is 20. 
Example 3: Verify the relationship between GCF and LCM of 15 and 20.
Solution:
The relation between GCF and LCM of 15 and 20 is given as,
LCM(15, 20) × GCF(15, 20) = Product of 15, 20
Prime factorization of 15 and 20 is given as, 15 = (3 × 5) = 3^{1} × 5^{1} and 20 = (2 × 2 × 5) = 2^{2} × 5^{1}
LCM(15, 20) = 60
GCF(15, 20) = 5
LHS = LCM(15, 20) × GCF(15, 20) = 60 × 5 = 300
RHS = Product of 15, 20 = 15 × 20 = 300
⇒ LHS = RHS = 300
Hence, verified.
FAQs on LCM of 15 and 20
What is the LCM of 15 and 20?
The LCM of 15 and 20 is 60. To find the LCM (least common multiple) of 15 and 20, we need to find the multiples of 15 and 20 (multiples of 15 = 15, 30, 45, 60; multiples of 20 = 20, 40, 60, 80) and choose the smallest multiple that is exactly divisible by 15 and 20, i.e., 60.
Which of the following is the LCM of 15 and 20? 25, 18, 35, 60
The value of LCM of 15, 20 is the smallest common multiple of 15 and 20. The number satisfying the given condition is 60.
If the LCM of 20 and 15 is 60, Find its GCF.
LCM(20, 15) × GCF(20, 15) = 20 × 15
Since the LCM of 20 and 15 = 60
⇒ 60 × GCF(20, 15) = 300
Therefore, the greatest common factor (GCF) = 300/60 = 5.
What is the Relation Between GCF and LCM of 15, 20?
The following equation can be used to express the relation between GCF and LCM of 15 and 20, i.e. GCF × LCM = 15 × 20.
What are the Methods to Find LCM of 15 and 20?
The commonly used methods to find the LCM of 15 and 20 are:
 Division Method
 Prime Factorization Method
 Listing Multiples