LCM of 42 and 48
LCM of 42 and 48 is the smallest number among all common multiples of 42 and 48. The first few multiples of 42 and 48 are (42, 84, 126, 168, . . . ) and (48, 96, 144, 192, 240, 288, . . . ) respectively. There are 3 commonly used methods to find LCM of 42 and 48  by division method, by listing multiples, and by prime factorization.
1.  LCM of 42 and 48 
2.  List of Methods 
3.  Solved Examples 
4.  FAQs 
What is the LCM of 42 and 48?
Answer: LCM of 42 and 48 is 336.
Explanation:
The LCM of two nonzero integers, x(42) and y(48), is the smallest positive integer m(336) that is divisible by both x(42) and y(48) without any remainder.
Methods to Find LCM of 42 and 48
Let's look at the different methods for finding the LCM of 42 and 48.
 By Prime Factorization Method
 By Division Method
 By Listing Multiples
LCM of 42 and 48 by Prime Factorization
Prime factorization of 42 and 48 is (2 × 3 × 7) = 2^{1} × 3^{1} × 7^{1} and (2 × 2 × 2 × 2 × 3) = 2^{4} × 3^{1} respectively. LCM of 42 and 48 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2^{4} × 3^{1} × 7^{1} = 336.
Hence, the LCM of 42 and 48 by prime factorization is 336.
LCM of 42 and 48 by Division Method
To calculate the LCM of 42 and 48 by the division method, we will divide the numbers(42, 48) by their prime factors (preferably common). The product of these divisors gives the LCM of 42 and 48.
 Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 42 and 48. Write this prime number(2) on the left of the given numbers(42 and 48), separated as per the ladder arrangement.
 Step 2: If any of the given numbers (42, 48) 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 48 is the product of all prime numbers on the left, i.e. LCM(42, 48) by division method = 2 × 2 × 2 × 2 × 3 × 7 = 336.
LCM of 42 and 48 by Listing Multiples
To calculate the LCM of 42 and 48 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, . . . ) and 48 (48, 96, 144, 192, 240, 288, . . . . )
 Step 2: The common multiples from the multiples of 42 and 48 are 336, 672, . . .
 Step 3: The smallest common multiple of 42 and 48 is 336.
∴ The least common multiple of 42 and 48 = 336.
☛ Also Check:
 LCM of 12 and 32  96
 LCM of 25, 40 and 60  600
 LCM of 2 and 12  12
 LCM of 6, 72 and 120  360
 LCM of 16 and 36  144
 LCM of 16 and 28  112
 LCM of 20, 40 and 60  120
LCM of 42 and 48 Examples

Example 1: The product of two numbers is 2016. If their GCD is 6, what is their LCM?
Solution:
Given: GCD = 6
product of numbers = 2016
∵ LCM × GCD = product of numbers
⇒ LCM = Product/GCD = 2016/6
Therefore, the LCM is 336.
The probable combination for the given case is LCM(42, 48) = 336. 
Example 2: Find the smallest number that is divisible by 42 and 48 exactly.
Solution:
The smallest number that is divisible by 42 and 48 exactly is their LCM.
⇒ Multiples of 42 and 48: Multiples of 42 = 42, 84, 126, 168, 210, 252, 294, 336, . . . .
 Multiples of 48 = 48, 96, 144, 192, 240, 288, 336, . . . .
Therefore, the LCM of 42 and 48 is 336.

Example 3: The GCD and LCM of two numbers are 6 and 336 respectively. If one number is 48, find the other number.
Solution:
Let the other number be p.
∵ GCD × LCM = 48 × p
⇒ p = (GCD × LCM)/48
⇒ p = (6 × 336)/48
⇒ p = 42
Therefore, the other number is 42.
FAQs on LCM of 42 and 48
What is the LCM of 42 and 48?
The LCM of 42 and 48 is 336. To find the LCM (least common multiple) of 42 and 48, we need to find the multiples of 42 and 48 (multiples of 42 = 42, 84, 126, 168 . . . . 336; multiples of 48 = 48, 96, 144, 192 . . . . 336) and choose the smallest multiple that is exactly divisible by 42 and 48, i.e., 336.
How to Find the LCM of 42 and 48 by Prime Factorization?
To find the LCM of 42 and 48 using prime factorization, we will find the prime factors, (42 = 2 × 3 × 7) and (48 = 2 × 2 × 2 × 2 × 3). LCM of 42 and 48 is the product of prime factors raised to their respective highest exponent among the numbers 42 and 48.
⇒ LCM of 42, 48 = 2^{4} × 3^{1} × 7^{1} = 336.
What is the Least Perfect Square Divisible by 42 and 48?
The least number divisible by 42 and 48 = LCM(42, 48)
LCM of 42 and 48 = 2 × 2 × 2 × 2 × 3 × 7 [Incomplete pair(s): 3, 7]
⇒ Least perfect square divisible by each 42 and 48 = LCM(42, 48) × 3 × 7 = 7056 [Square root of 7056 = √7056 = ±84]
Therefore, 7056 is the required number.
If the LCM of 48 and 42 is 336, Find its GCF.
LCM(48, 42) × GCF(48, 42) = 48 × 42
Since the LCM of 48 and 42 = 336
⇒ 336 × GCF(48, 42) = 2016
Therefore, the GCF (greatest common factor) = 2016/336 = 6.
What are the Methods to Find LCM of 42 and 48?
The commonly used methods to find the LCM of 42 and 48 are:
 Division Method
 Prime Factorization Method
 Listing Multiples