LCM of 15 and 18
LCM of 15 and 18 is the smallest number among all common multiples of 15 and 18. The first few multiples of 15 and 18 are (15, 30, 45, 60, 75, 90, . . . ) and (18, 36, 54, 72, 90, . . . ) respectively. There are 3 commonly used methods to find LCM of 15 and 18  by division method, by prime factorization, and by listing multiples.
1.  LCM of 15 and 18 
2.  List of Methods 
3.  Solved Examples 
4.  FAQs 
What is the LCM of 15 and 18?
Answer: LCM of 15 and 18 is 90.
Explanation:
The LCM of two nonzero integers, x(15) and y(18), is the smallest positive integer m(90) that is divisible by both x(15) and y(18) without any remainder.
Methods to Find LCM of 15 and 18
The methods to find the LCM of 15 and 18 are explained below.
 By Listing Multiples
 By Prime Factorization Method
 By Division Method
LCM of 15 and 18 by Listing Multiples
To calculate the LCM of 15 and 18 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 18 (18, 36, 54, 72, 90, . . . . )
 Step 2: The common multiples from the multiples of 15 and 18 are 90, 180, . . .
 Step 3: The smallest common multiple of 15 and 18 is 90.
∴ The least common multiple of 15 and 18 = 90.
LCM of 15 and 18 by Prime Factorization
Prime factorization of 15 and 18 is (3 × 5) = 3^{1} × 5^{1} and (2 × 3 × 3) = 2^{1} × 3^{2} respectively. LCM of 15 and 18 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2^{1} × 3^{2} × 5^{1} = 90.
Hence, the LCM of 15 and 18 by prime factorization is 90.
LCM of 15 and 18 by Division Method
To calculate the LCM of 15 and 18 by the division method, we will divide the numbers(15, 18) by their prime factors (preferably common). The product of these divisors gives the LCM of 15 and 18.
 Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 15 and 18. Write this prime number(2) on the left of the given numbers(15 and 18), separated as per the ladder arrangement.
 Step 2: If any of the given numbers (15, 18) 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 18 is the product of all prime numbers on the left, i.e. LCM(15, 18) by division method = 2 × 3 × 3 × 5 = 90.
☛ Also Check:
 LCM of 4 and 22  44
 LCM of 4 and 20  20
 LCM of 4 and 18  36
 LCM of 4 and 16  16
 LCM of 4 and 15  60
 LCM of 4 and 14  28
 LCM of 4 and 13  52
LCM of 15 and 18 Examples

Example 1: The product of two numbers is 270. If their GCD is 3, what is their LCM?
Solution:
Given: GCD = 3
product of numbers = 270
∵ LCM × GCD = product of numbers
⇒ LCM = Product/GCD = 270/3
Therefore, the LCM is 90.
The probable combination for the given case is LCM(15, 18) = 90. 
Example 2: Verify the relationship between GCF and LCM of 15 and 18.
Solution:
The relation between GCF and LCM of 15 and 18 is given as,
LCM(15, 18) × GCF(15, 18) = Product of 15, 18
Prime factorization of 15 and 18 is given as, 15 = (3 × 5) = 3^{1} × 5^{1} and 18 = (2 × 3 × 3) = 2^{1} × 3^{2}
LCM(15, 18) = 90
GCF(15, 18) = 3
LHS = LCM(15, 18) × GCF(15, 18) = 90 × 3 = 270
RHS = Product of 15, 18 = 15 × 18 = 270
⇒ LHS = RHS = 270
Hence, verified. 
Example 3: Find the smallest number that is divisible by 15 and 18 exactly.
Solution:
The smallest number that is divisible by 15 and 18 exactly is their LCM.
⇒ Multiples of 15 and 18: Multiples of 15 = 15, 30, 45, 60, 75, 90, 105, . . . .
 Multiples of 18 = 18, 36, 54, 72, 90, 108, 126, . . . .
Therefore, the LCM of 15 and 18 is 90.
FAQs on LCM of 15 and 18
What is the LCM of 15 and 18?
The LCM of 15 and 18 is 90. To find the LCM of 15 and 18, we need to find the multiples of 15 and 18 (multiples of 15 = 15, 30, 45, 60 . . . . 90; multiples of 18 = 18, 36, 54, 72 . . . . 90) and choose the smallest multiple that is exactly divisible by 15 and 18, i.e., 90.
What is the Least Perfect Square Divisible by 15 and 18?
The least number divisible by 15 and 18 = LCM(15, 18)
LCM of 15 and 18 = 2 × 3 × 3 × 5 [Incomplete pair(s): 2, 5]
⇒ Least perfect square divisible by each 15 and 18 = LCM(15, 18) × 2 × 5 = 900 [Square root of 900 = √900 = ±30]
Therefore, 900 is the required number.
Which of the following is the LCM of 15 and 18? 90, 50, 12, 35
The value of LCM of 15, 18 is the smallest common multiple of 15 and 18. The number satisfying the given condition is 90.
If the LCM of 18 and 15 is 90, Find its GCF.
LCM(18, 15) × GCF(18, 15) = 18 × 15
Since the LCM of 18 and 15 = 90
⇒ 90 × GCF(18, 15) = 270
Therefore, the GCF = 270/90 = 3.
What are the Methods to Find LCM of 15 and 18?
The commonly used methods to find the LCM of 15 and 18 are:
 Division Method
 Listing Multiples
 Prime Factorization Method
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