LCM of 48 and 56

LCM of 48 and 56 is the smallest number among all common multiples of 48 and 56. The first few multiples of 48 and 56 are (48, 96, 144, 192, 240, . . . ) and (56, 112, 168, 224, 280, 336, 392, . . . ) respectively. There are 3 commonly used methods to find LCM of 48 and 56 - by prime factorization, by division method, and by listing multiples.

Answer: LCM of 48 and 56 is 336.

Explanation:

The LCM of two non-zero integers, x(48) and y(56), is the smallest positive integer m(336) that is divisible by both x(48) and y(56) without any remainder.

Let's look at the different methods for finding the LCM of 48 and 56.

• By Division Method
• By Listing Multiples
• By Prime Factorization Method

LCM of 48 and 56 by Division Method

To calculate the LCM of 48 and 56 by the division method, we will divide the numbers(48, 56) by their prime factors (preferably common). The product of these divisors gives the LCM of 48 and 56.

• Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 48 and 56. Write this prime number(2) on the left of the given numbers(48 and 56), separated as per the ladder arrangement.
• Step 2: If any of the given numbers (48, 56) 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 48 and 56 is the product of all prime numbers on the left, i.e. LCM(48, 56) by division method = 2 × 2 × 2 × 2 × 3 × 7 = 336.

LCM of 48 and 56 by Listing Multiples

To calculate the LCM of 48 and 56 by listing out the common multiples, we can follow the given below steps:

• Step 1: List a few multiples of 48 (48, 96, 144, 192, 240, . . . ) and 56 (56, 112, 168, 224, 280, 336, 392, . . . . )
• Step 2: The common multiples from the multiples of 48 and 56 are 336, 672, . . .
• Step 3: The smallest common multiple of 48 and 56 is 336.

∴ The least common multiple of 48 and 56 = 336.

LCM of 48 and 56 by Prime Factorization

Prime factorization of 48 and 56 is (2 × 2 × 2 × 2 × 3) = 2⁴ × 3¹ and (2 × 2 × 2 × 7) = 2³ × 7¹ respectively. LCM of 48 and 56 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2⁴ × 3¹ × 7¹ = 336.
Hence, the LCM of 48 and 56 by prime factorization is 336.

☛ Also Check:

• LCM of 25 and 35 - 175
• LCM of 10, 25, 35 and 40 - 1400
• LCM of 2923 and 3239 - 119843
• LCM of 4 and 16 - 16
• LCM of 3 and 4 - 12
• LCM of 11 and 13 - 143
• LCM of 25 and 30 - 150

FAQs on LCM of 48 and 56

What is the LCM of 48 and 56?

The LCM of 48 and 56 is 336. To find the LCM of 48 and 56, we need to find the multiples of 48 and 56 (multiples of 48 = 48, 96, 144, 192 . . . . 336; multiples of 56 = 56, 112, 168, 224 . . . . 336) and choose the smallest multiple that is exactly divisible by 48 and 56, i.e., 336.

If the LCM of 56 and 48 is 336, Find its GCF.

LCM(56, 48) × GCF(56, 48) = 56 × 48
Since the LCM of 56 and 48 = 336
⇒ 336 × GCF(56, 48) = 2688
Therefore, the greatest common factor (GCF) = 2688/336 = 8.

What is the Least Perfect Square Divisible by 48 and 56?

The least number divisible by 48 and 56 = LCM(48, 56)
LCM of 48 and 56 = 2 × 2 × 2 × 2 × 3 × 7 [Incomplete pair(s): 3, 7]
⇒ Least perfect square divisible by each 48 and 56 = LCM(48, 56) × 3 × 7 = 7056 [Square root of 7056 = √7056 = ±84]
Therefore, 7056 is the required number.

How to Find the LCM of 48 and 56 by Prime Factorization?

To find the LCM of 48 and 56 using prime factorization, we will find the prime factors, (48 = 2 × 2 × 2 × 2 × 3) and (56 = 2 × 2 × 2 × 7). LCM of 48 and 56 is the product of prime factors raised to their respective highest exponent among the numbers 48 and 56.
⇒ LCM of 48, 56 = 2⁴ × 3¹ × 7¹ = 336.

What is the Relation Between GCF and LCM of 48, 56?

The following equation can be used to express the relation between GCF and LCM of 48 and 56, i.e. GCF × LCM = 48 × 56.