LCM of 6 and 18
LCM of 6 and 18 is the smallest number among all common multiples of 6 and 18. The first few multiples of 6 and 18 are (6, 12, 18, 24, 30, 36, . . . ) and (18, 36, 54, 72, . . . ) respectively. There are 3 commonly used methods to find LCM of 6 and 18  by prime factorization, by listing multiples, and by division method.
1.  LCM of 6 and 18 
2.  List of Methods 
3.  Solved Examples 
4.  FAQs 
What is the LCM of 6 and 18?
Answer: LCM of 6 and 18 is 18.
Explanation:
The LCM of two nonzero integers, x(6) and y(18), is the smallest positive integer m(18) that is divisible by both x(6) and y(18) without any remainder.
Methods to Find LCM of 6 and 18
Let's look at the different methods for finding the LCM of 6 and 18.
 By Prime Factorization Method
 By Listing Multiples
 By Division Method
LCM of 6 and 18 by Prime Factorization
Prime factorization of 6 and 18 is (2 × 3) = 2^{1} × 3^{1} and (2 × 3 × 3) = 2^{1} × 3^{2} respectively. LCM of 6 and 18 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2^{1} × 3^{2} = 18.
Hence, the LCM of 6 and 18 by prime factorization is 18.
LCM of 6 and 18 by Listing Multiples
To calculate the LCM of 6 and 18 by listing out the common multiples, we can follow the given below steps:
 Step 1: List a few multiples of 6 (6, 12, 18, 24, 30, 36, . . . ) and 18 (18, 36, 54, 72, . . . . )
 Step 2: The common multiples from the multiples of 6 and 18 are 18, 36, . . .
 Step 3: The smallest common multiple of 6 and 18 is 18.
∴ The least common multiple of 6 and 18 = 18.
LCM of 6 and 18 by Division Method
To calculate the LCM of 6 and 18 by the division method, we will divide the numbers(6, 18) by their prime factors (preferably common). The product of these divisors gives the LCM of 6 and 18.
 Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 6 and 18. Write this prime number(2) on the left of the given numbers(6 and 18), separated as per the ladder arrangement.
 Step 2: If any of the given numbers (6, 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 6 and 18 is the product of all prime numbers on the left, i.e. LCM(6, 18) by division method = 2 × 3 × 3 = 18.
☛ Also Check:
 LCM of 9, 12 and 15  180
 LCM of 10 and 11  110
 LCM of 15 and 27  135
 LCM of 19 and 57  57
 LCM of 2, 4 and 5  20
 LCM of 9 and 13  117
 LCM of 25 and 35  175
LCM of 6 and 18 Examples

Example 1: Find the smallest number that is divisible by 6 and 18 exactly.
Solution:
The smallest number that is divisible by 6 and 18 exactly is their LCM.
⇒ Multiples of 6 and 18: Multiples of 6 = 6, 12, 18, 24, 30, . . . .
 Multiples of 18 = 18, 36, 54, 72, 90, . . . .
Therefore, the LCM of 6 and 18 is 18.

Example 2: The product of two numbers is 108. If their GCD is 6, what is their LCM?
Solution:
Given: GCD = 6
product of numbers = 108
∵ LCM × GCD = product of numbers
⇒ LCM = Product/GCD = 108/6
Therefore, the LCM is 18.
The probable combination for the given case is LCM(6, 18) = 18. 
Example 3: The GCD and LCM of two numbers are 6 and 18 respectively. If one number is 6, find the other number.
Solution:
Let the other number be m.
∵ GCD × LCM = 6 × m
⇒ m = (GCD × LCM)/6
⇒ m = (6 × 18)/6
⇒ m = 18
Therefore, the other number is 18.
FAQs on LCM of 6 and 18
What is the LCM of 6 and 18?
The LCM of 6 and 18 is 18. To find the least common multiple (LCM) of 6 and 18, we need to find the multiples of 6 and 18 (multiples of 6 = 6, 12, 18, 24; multiples of 18 = 18, 36, 54, 72) and choose the smallest multiple that is exactly divisible by 6 and 18, i.e., 18.
If the LCM of 18 and 6 is 18, Find its GCF.
LCM(18, 6) × GCF(18, 6) = 18 × 6
Since the LCM of 18 and 6 = 18
⇒ 18 × GCF(18, 6) = 108
Therefore, the GCF = 108/18 = 6.
What is the Relation Between GCF and LCM of 6, 18?
The following equation can be used to express the relation between GCF and LCM of 6 and 18, i.e. GCF × LCM = 6 × 18.
What is the Least Perfect Square Divisible by 6 and 18?
The least number divisible by 6 and 18 = LCM(6, 18)
LCM of 6 and 18 = 2 × 3 × 3 [Incomplete pair(s): 2]
⇒ Least perfect square divisible by each 6 and 18 = LCM(6, 18) × 2 = 36 [Square root of 36 = √36 = ±6]
Therefore, 36 is the required number.
How to Find the LCM of 6 and 18 by Prime Factorization?
To find the LCM of 6 and 18 using prime factorization, we will find the prime factors, (6 = 2 × 3) and (18 = 2 × 3 × 3). LCM of 6 and 18 is the product of prime factors raised to their respective highest exponent among the numbers 6 and 18.
⇒ LCM of 6, 18 = 2^{1} × 3^{2} = 18.
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