LCM of 11 and 18
LCM of 11 and 18 is the smallest number among all common multiples of 11 and 18. The first few multiples of 11 and 18 are (11, 22, 33, 44, . . . ) and (18, 36, 54, 72, . . . ) respectively. There are 3 commonly used methods to find LCM of 11 and 18  by prime factorization, by listing multiples, and by division method.
1.  LCM of 11 and 18 
2.  List of Methods 
3.  Solved Examples 
4.  FAQs 
What is the LCM of 11 and 18?
Answer: LCM of 11 and 18 is 198.
Explanation:
The LCM of two nonzero integers, x(11) and y(18), is the smallest positive integer m(198) that is divisible by both x(11) and y(18) without any remainder.
Methods to Find LCM of 11 and 18
The methods to find the LCM of 11 and 18 are explained below.
 By Listing Multiples
 By Division Method
 By Prime Factorization Method
LCM of 11 and 18 by Listing Multiples
To calculate the LCM of 11 and 18 by listing out the common multiples, we can follow the given below steps:
 Step 1: List a few multiples of 11 (11, 22, 33, 44, . . . ) and 18 (18, 36, 54, 72, . . . . )
 Step 2: The common multiples from the multiples of 11 and 18 are 198, 396, . . .
 Step 3: The smallest common multiple of 11 and 18 is 198.
∴ The least common multiple of 11 and 18 = 198.
LCM of 11 and 18 by Division Method
To calculate the LCM of 11 and 18 by the division method, we will divide the numbers(11, 18) by their prime factors (preferably common). The product of these divisors gives the LCM of 11 and 18.
 Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 11 and 18. Write this prime number(2) on the left of the given numbers(11 and 18), separated as per the ladder arrangement.
 Step 2: If any of the given numbers (11, 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 11 and 18 is the product of all prime numbers on the left, i.e. LCM(11, 18) by division method = 2 × 3 × 3 × 11 = 198.
LCM of 11 and 18 by Prime Factorization
Prime factorization of 11 and 18 is (11) = 11^{1} and (2 × 3 × 3) = 2^{1} × 3^{2} respectively. LCM of 11 and 18 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2^{1} × 3^{2} × 11^{1} = 198.
Hence, the LCM of 11 and 18 by prime factorization is 198.
☛ Also Check:
 LCM of 25 and 50  50
 LCM of 25 and 45  225
 LCM of 25 and 40  200
 LCM of 25 and 36  900
 LCM of 25 and 35  175
 LCM of 25 and 30  150
 LCM of 25 and 100  100
LCM of 11 and 18 Examples

Example 1: Find the smallest number that is divisible by 11 and 18 exactly.
Solution:
The value of LCM(11, 18) will be the smallest number that is exactly divisible by 11 and 18.
⇒ Multiples of 11 and 18: Multiples of 11 = 11, 22, 33, 44, 55, 66, 77, 88, 99, 110, . . . ., 154, 165, 176, 187, 198, . . . .
 Multiples of 18 = 18, 36, 54, 72, 90, 108, 126, 144, 162, 180, . . . ., 126, 144, 162, 180, 198, . . . .
Therefore, the LCM of 11 and 18 is 198.

Example 2: The product of two numbers is 198. If their GCD is 1, what is their LCM?
Solution:
Given: GCD = 1
product of numbers = 198
∵ LCM × GCD = product of numbers
⇒ LCM = Product/GCD = 198/1
Therefore, the LCM is 198.
The probable combination for the given case is LCM(11, 18) = 198. 
Example 3: Verify the relationship between GCF and LCM of 11 and 18.
Solution:
The relation between GCF and LCM of 11 and 18 is given as,
LCM(11, 18) × GCF(11, 18) = Product of 11, 18
Prime factorization of 11 and 18 is given as, 11 = (11) = 11^{1} and 18 = (2 × 3 × 3) = 2^{1} × 3^{2}
LCM(11, 18) = 198
GCF(11, 18) = 1
LHS = LCM(11, 18) × GCF(11, 18) = 198 × 1 = 198
RHS = Product of 11, 18 = 11 × 18 = 198
⇒ LHS = RHS = 198
Hence, verified.
FAQs on LCM of 11 and 18
What is the LCM of 11 and 18?
The LCM of 11 and 18 is 198. To find the least common multiple of 11 and 18, we need to find the multiples of 11 and 18 (multiples of 11 = 11, 22, 33, 44 . . . . 198; multiples of 18 = 18, 36, 54, 72 . . . . 198) and choose the smallest multiple that is exactly divisible by 11 and 18, i.e., 198.
Which of the following is the LCM of 11 and 18? 12, 30, 198, 50
The value of LCM of 11, 18 is the smallest common multiple of 11 and 18. The number satisfying the given condition is 198.
How to Find the LCM of 11 and 18 by Prime Factorization?
To find the LCM of 11 and 18 using prime factorization, we will find the prime factors, (11 = 11) and (18 = 2 × 3 × 3). LCM of 11 and 18 is the product of prime factors raised to their respective highest exponent among the numbers 11 and 18.
⇒ LCM of 11, 18 = 2^{1} × 3^{2} × 11^{1} = 198.
If the LCM of 18 and 11 is 198, Find its GCF.
LCM(18, 11) × GCF(18, 11) = 18 × 11
Since the LCM of 18 and 11 = 198
⇒ 198 × GCF(18, 11) = 198
Therefore, the greatest common factor (GCF) = 198/198 = 1.
What are the Methods to Find LCM of 11 and 18?
The commonly used methods to find the LCM of 11 and 18 are:
 Prime Factorization Method
 Division Method
 Listing Multiples