LCM of 18 and 36
LCM of 18 and 36 is the smallest number among all common multiples of 18 and 36. The first few multiples of 18 and 36 are (18, 36, 54, 72, 90, 108, . . . ) and (36, 72, 108, 144, 180, 216, 252, . . . ) respectively. There are 3 commonly used methods to find LCM of 18 and 36  by division method, by prime factorization, and by listing multiples.
1.  LCM of 18 and 36 
2.  List of Methods 
3.  Solved Examples 
4.  FAQs 
What is the LCM of 18 and 36?
Answer: LCM of 18 and 36 is 36.
Explanation:
The LCM of two nonzero integers, x(18) and y(36), is the smallest positive integer m(36) that is divisible by both x(18) and y(36) without any remainder.
Methods to Find LCM of 18 and 36
Let's look at the different methods for finding the LCM of 18 and 36.
 By Prime Factorization Method
 By Listing Multiples
 By Division Method
LCM of 18 and 36 by Prime Factorization
Prime factorization of 18 and 36 is (2 × 3 × 3) = 2^{1} × 3^{2} and (2 × 2 × 3 × 3) = 2^{2} × 3^{2} respectively. LCM of 18 and 36 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2^{2} × 3^{2} = 36.
Hence, the LCM of 18 and 36 by prime factorization is 36.
LCM of 18 and 36 by Listing Multiples
To calculate the LCM of 18 and 36 by listing out the common multiples, we can follow the given below steps:
 Step 1: List a few multiples of 18 (18, 36, 54, 72, 90, 108, . . . ) and 36 (36, 72, 108, 144, 180, 216, 252, . . . . )
 Step 2: The common multiples from the multiples of 18 and 36 are 36, 72, . . .
 Step 3: The smallest common multiple of 18 and 36 is 36.
∴ The least common multiple of 18 and 36 = 36.
LCM of 18 and 36 by Division Method
To calculate the LCM of 18 and 36 by the division method, we will divide the numbers(18, 36) by their prime factors (preferably common). The product of these divisors gives the LCM of 18 and 36.
 Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 18 and 36. Write this prime number(2) on the left of the given numbers(18 and 36), separated as per the ladder arrangement.
 Step 2: If any of the given numbers (18, 36) 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 18 and 36 is the product of all prime numbers on the left, i.e. LCM(18, 36) by division method = 2 × 2 × 3 × 3 = 36.
☛ Also Check:
 LCM of 3 and 13  39
 LCM of 80, 85 and 90  12240
 LCM of 18 and 28  252
 LCM of 2 and 13  26
 LCM of 8 and 9  72
 LCM of 16, 28 and 40  560
 LCM of 21 and 35  105
LCM of 18 and 36 Examples

Example 1: Verify the relationship between GCF and LCM of 18 and 36.
Solution:
The relation between GCF and LCM of 18 and 36 is given as,
LCM(18, 36) × GCF(18, 36) = Product of 18, 36
Prime factorization of 18 and 36 is given as, 18 = (2 × 3 × 3) = 2^{1} × 3^{2} and 36 = (2 × 2 × 3 × 3) = 2^{2} × 3^{2}
LCM(18, 36) = 36
GCF(18, 36) = 18
LHS = LCM(18, 36) × GCF(18, 36) = 36 × 18 = 648
RHS = Product of 18, 36 = 18 × 36 = 648
⇒ LHS = RHS = 648
Hence, verified. 
Example 2: The GCD and LCM of two numbers are 18 and 36 respectively. If one number is 36, find the other number.
Solution:
Let the other number be b.
∵ GCD × LCM = 36 × b
⇒ b = (GCD × LCM)/36
⇒ b = (18 × 36)/36
⇒ b = 18
Therefore, the other number is 18. 
Example 3: Find the smallest number that is divisible by 18 and 36 exactly.
Solution:
The smallest number that is divisible by 18 and 36 exactly is their LCM.
⇒ Multiples of 18 and 36: Multiples of 18 = 18, 36, 54, 72, 90, . . . .
 Multiples of 36 = 36, 72, 108, 144, 180, . . . .
Therefore, the LCM of 18 and 36 is 36.
FAQs on LCM of 18 and 36
What is the LCM of 18 and 36?
The LCM of 18 and 36 is 36. To find the LCM (least common multiple) of 18 and 36, we need to find the multiples of 18 and 36 (multiples of 18 = 18, 36, 54, 72; multiples of 36 = 36, 72, 108, 144) and choose the smallest multiple that is exactly divisible by 18 and 36, i.e., 36.
Which of the following is the LCM of 18 and 36? 30, 36, 5, 21
The value of LCM of 18, 36 is the smallest common multiple of 18 and 36. The number satisfying the given condition is 36.
How to Find the LCM of 18 and 36 by Prime Factorization?
To find the LCM of 18 and 36 using prime factorization, we will find the prime factors, (18 = 2 × 3 × 3) and (36 = 2 × 2 × 3 × 3). LCM of 18 and 36 is the product of prime factors raised to their respective highest exponent among the numbers 18 and 36.
⇒ LCM of 18, 36 = 2^{2} × 3^{2} = 36.
If the LCM of 36 and 18 is 36, Find its GCF.
LCM(36, 18) × GCF(36, 18) = 36 × 18
Since the LCM of 36 and 18 = 36
⇒ 36 × GCF(36, 18) = 648
Therefore, the greatest common factor = 648/36 = 18.
What is the Least Perfect Square Divisible by 18 and 36?
The least number divisible by 18 and 36 = LCM(18, 36)
LCM of 18 and 36 = 2 × 2 × 3 × 3 [No incomplete pair]
⇒ Least perfect square divisible by each 18 and 36 = 36 [Square root of 36 = √36 = ±6]
Therefore, 36 is the required number.
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