LCM of 18 and 42
LCM of 18 and 42 is the smallest number among all common multiples of 18 and 42. The first few multiples of 18 and 42 are (18, 36, 54, 72, 90, 108, 126, . . . ) and (42, 84, 126, 168, . . . ) respectively. There are 3 commonly used methods to find LCM of 18 and 42  by listing multiples, by division method, and by prime factorization.
1.  LCM of 18 and 42 
2.  List of Methods 
3.  Solved Examples 
4.  FAQs 
What is the LCM of 18 and 42?
Answer: LCM of 18 and 42 is 126.
Explanation:
The LCM of two nonzero integers, x(18) and y(42), is the smallest positive integer m(126) that is divisible by both x(18) and y(42) without any remainder.
Methods to Find LCM of 18 and 42
The methods to find the LCM of 18 and 42 are explained below.
 By Prime Factorization Method
 By Listing Multiples
 By Division Method
LCM of 18 and 42 by Prime Factorization
Prime factorization of 18 and 42 is (2 × 3 × 3) = 2^{1} × 3^{2} and (2 × 3 × 7) = 2^{1} × 3^{1} × 7^{1} respectively. LCM of 18 and 42 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2^{1} × 3^{2} × 7^{1} = 126.
Hence, the LCM of 18 and 42 by prime factorization is 126.
LCM of 18 and 42 by Listing Multiples
To calculate the LCM of 18 and 42 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, 126, . . . ) and 42 (42, 84, 126, 168, . . . . )
 Step 2: The common multiples from the multiples of 18 and 42 are 126, 252, . . .
 Step 3: The smallest common multiple of 18 and 42 is 126.
∴ The least common multiple of 18 and 42 = 126.
LCM of 18 and 42 by Division Method
To calculate the LCM of 18 and 42 by the division method, we will divide the numbers(18, 42) by their prime factors (preferably common). The product of these divisors gives the LCM of 18 and 42.
 Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 18 and 42. Write this prime number(2) on the left of the given numbers(18 and 42), separated as per the ladder arrangement.
 Step 2: If any of the given numbers (18, 42) 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 42 is the product of all prime numbers on the left, i.e. LCM(18, 42) by division method = 2 × 3 × 3 × 7 = 126.
☛ Also Check:
 LCM of 8, 9 and 12  72
 LCM of 5 and 16  80
 LCM of 5, 8 and 15  120
 LCM of 3 and 11  33
 LCM of 8, 9 and 25  1800
 LCM of 36 and 64  576
 LCM of 12, 15 and 20  60
LCM of 18 and 42 Examples

Example 1: Verify the relationship between GCF and LCM of 18 and 42.
Solution:
The relation between GCF and LCM of 18 and 42 is given as,
LCM(18, 42) × GCF(18, 42) = Product of 18, 42
Prime factorization of 18 and 42 is given as, 18 = (2 × 3 × 3) = 2^{1} × 3^{2} and 42 = (2 × 3 × 7) = 2^{1} × 3^{1} × 7^{1}
LCM(18, 42) = 126
GCF(18, 42) = 6
LHS = LCM(18, 42) × GCF(18, 42) = 126 × 6 = 756
RHS = Product of 18, 42 = 18 × 42 = 756
⇒ LHS = RHS = 756
Hence, verified. 
Example 2: The GCD and LCM of two numbers are 6 and 126 respectively. If one number is 42, find the other number.
Solution:
Let the other number be z.
∵ GCD × LCM = 42 × z
⇒ z = (GCD × LCM)/42
⇒ z = (6 × 126)/42
⇒ z = 18
Therefore, the other number is 18. 
Example 3: Find the smallest number that is divisible by 18 and 42 exactly.
Solution:
The smallest number that is divisible by 18 and 42 exactly is their LCM.
⇒ Multiples of 18 and 42: Multiples of 18 = 18, 36, 54, 72, 90, 108, 126, . . . .
 Multiples of 42 = 42, 84, 126, 168, 210, . . . .
Therefore, the LCM of 18 and 42 is 126.
FAQs on LCM of 18 and 42
What is the LCM of 18 and 42?
The LCM of 18 and 42 is 126. To find the LCM (least common multiple) of 18 and 42, we need to find the multiples of 18 and 42 (multiples of 18 = 18, 36, 54, 72 . . . . 126; multiples of 42 = 42, 84, 126, 168) and choose the smallest multiple that is exactly divisible by 18 and 42, i.e., 126.
What are the Methods to Find LCM of 18 and 42?
The commonly used methods to find the LCM of 18 and 42 are:
 Division Method
 Listing Multiples
 Prime Factorization Method
If the LCM of 42 and 18 is 126, Find its GCF.
LCM(42, 18) × GCF(42, 18) = 42 × 18
Since the LCM of 42 and 18 = 126
⇒ 126 × GCF(42, 18) = 756
Therefore, the greatest common factor = 756/126 = 6.
How to Find the LCM of 18 and 42 by Prime Factorization?
To find the LCM of 18 and 42 using prime factorization, we will find the prime factors, (18 = 2 × 3 × 3) and (42 = 2 × 3 × 7). LCM of 18 and 42 is the product of prime factors raised to their respective highest exponent among the numbers 18 and 42.
⇒ LCM of 18, 42 = 2^{1} × 3^{2} × 7^{1} = 126.
Which of the following is the LCM of 18 and 42? 42, 10, 126, 36
The value of LCM of 18, 42 is the smallest common multiple of 18 and 42. The number satisfying the given condition is 126.
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