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.

Answer: LCM of 42 and 48 is 336.

Explanation:

The LCM of two non-zero 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.

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) = 2¹ × 3¹ × 7¹ and (2 × 2 × 2 × 2 × 3) = 2⁴ × 3¹ respectively. LCM of 42 and 48 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2⁴ × 3¹ × 7¹ = 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

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 = 2⁴ × 3¹ × 7¹ = 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