LCM of 42 and 54
LCM of 42 and 54 is the smallest number among all common multiples of 42 and 54. The first few multiples of 42 and 54 are (42, 84, 126, 168, 210, . . . ) and (54, 108, 162, 216, . . . ) respectively. There are 3 commonly used methods to find LCM of 42 and 54  by division method, by listing multiples, and by prime factorization.
1.  LCM of 42 and 54 
2.  List of Methods 
3.  Solved Examples 
4.  FAQs 
What is the LCM of 42 and 54?
Answer: LCM of 42 and 54 is 378.
Explanation:
The LCM of two nonzero integers, x(42) and y(54), is the smallest positive integer m(378) that is divisible by both x(42) and y(54) without any remainder.
Methods to Find LCM of 42 and 54
Let's look at the different methods for finding the LCM of 42 and 54.
 By Listing Multiples
 By Division Method
 By Prime Factorization Method
LCM of 42 and 54 by Listing Multiples
To calculate the LCM of 42 and 54 by listing out the common multiples, we can follow the given below steps:
 Step 1: List a few multiples of 42 (42, 84, 126, 168, 210, . . . ) and 54 (54, 108, 162, 216, . . . . )
 Step 2: The common multiples from the multiples of 42 and 54 are 378, 756, . . .
 Step 3: The smallest common multiple of 42 and 54 is 378.
∴ The least common multiple of 42 and 54 = 378.
LCM of 42 and 54 by Division Method
To calculate the LCM of 42 and 54 by the division method, we will divide the numbers(42, 54) by their prime factors (preferably common). The product of these divisors gives the LCM of 42 and 54.
 Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 42 and 54. Write this prime number(2) on the left of the given numbers(42 and 54), separated as per the ladder arrangement.
 Step 2: If any of the given numbers (42, 54) 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 42 and 54 is the product of all prime numbers on the left, i.e. LCM(42, 54) by division method = 2 × 3 × 3 × 3 × 7 = 378.
LCM of 42 and 54 by Prime Factorization
Prime factorization of 42 and 54 is (2 × 3 × 7) = 2^{1} × 3^{1} × 7^{1} and (2 × 3 × 3 × 3) = 2^{1} × 3^{3} respectively. LCM of 42 and 54 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2^{1} × 3^{3} × 7^{1} = 378.
Hence, the LCM of 42 and 54 by prime factorization is 378.
☛ Also Check:
 LCM of 2, 4, 6 and 8  24
 LCM of 6, 7 and 8  168
 LCM of 7 and 17  119
 LCM of 12 and 25  300
 LCM of 13 and 39  39
 LCM of 8 and 32  32
 LCM of 9 and 10  90
LCM of 42 and 54 Examples

Example 1: The product of two numbers is 2268. If their GCD is 6, what is their LCM?
Solution:
Given: GCD = 6
product of numbers = 2268
∵ LCM × GCD = product of numbers
⇒ LCM = Product/GCD = 2268/6
Therefore, the LCM is 378.
The probable combination for the given case is LCM(42, 54) = 378. 
Example 2: Find the smallest number that is divisible by 42 and 54 exactly.
Solution:
The smallest number that is divisible by 42 and 54 exactly is their LCM.
⇒ Multiples of 42 and 54: Multiples of 42 = 42, 84, 126, 168, 210, 252, 294, 336, 378, . . . .
 Multiples of 54 = 54, 108, 162, 216, 270, 324, 378, . . . .
Therefore, the LCM of 42 and 54 is 378.

Example 3: Verify the relationship between GCF and LCM of 42 and 54.
Solution:
The relation between GCF and LCM of 42 and 54 is given as,
LCM(42, 54) × GCF(42, 54) = Product of 42, 54
Prime factorization of 42 and 54 is given as, 42 = (2 × 3 × 7) = 2^{1} × 3^{1} × 7^{1} and 54 = (2 × 3 × 3 × 3) = 2^{1} × 3^{3}
LCM(42, 54) = 378
GCF(42, 54) = 6
LHS = LCM(42, 54) × GCF(42, 54) = 378 × 6 = 2268
RHS = Product of 42, 54 = 42 × 54 = 2268
⇒ LHS = RHS = 2268
Hence, verified.
FAQs on LCM of 42 and 54
What is the LCM of 42 and 54?
The LCM of 42 and 54 is 378. To find the least common multiple of 42 and 54, we need to find the multiples of 42 and 54 (multiples of 42 = 42, 84, 126, 168 . . . . 378; multiples of 54 = 54, 108, 162, 216 . . . . 378) and choose the smallest multiple that is exactly divisible by 42 and 54, i.e., 378.
How to Find the LCM of 42 and 54 by Prime Factorization?
To find the LCM of 42 and 54 using prime factorization, we will find the prime factors, (42 = 2 × 3 × 7) and (54 = 2 × 3 × 3 × 3). LCM of 42 and 54 is the product of prime factors raised to their respective highest exponent among the numbers 42 and 54.
⇒ LCM of 42, 54 = 2^{1} × 3^{3} × 7^{1} = 378.
Which of the following is the LCM of 42 and 54? 3, 25, 42, 378
The value of LCM of 42, 54 is the smallest common multiple of 42 and 54. The number satisfying the given condition is 378.
What are the Methods to Find LCM of 42 and 54?
The commonly used methods to find the LCM of 42 and 54 are:
 Listing Multiples
 Prime Factorization Method
 Division Method
If the LCM of 54 and 42 is 378, Find its GCF.
LCM(54, 42) × GCF(54, 42) = 54 × 42
Since the LCM of 54 and 42 = 378
⇒ 378 × GCF(54, 42) = 2268
Therefore, the greatest common factor = 2268/378 = 6.