LCM of 56 and 84

LCM of 56 and 84 is the smallest number among all common multiples of 56 and 84. The first few multiples of 56 and 84 are (56, 112, 168, 224, 280, . . . ) and (84, 168, 252, 336, 420, 504, . . . ) respectively. There are 3 commonly used methods to find LCM of 56 and 84 - by prime factorization, by division method, and by listing multiples.

Answer: LCM of 56 and 84 is 168.

Explanation:

The LCM of two non-zero integers, x(56) and y(84), is the smallest positive integer m(168) that is divisible by both x(56) and y(84) without any remainder.

Let's look at the different methods for finding the LCM of 56 and 84.

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

LCM of 56 and 84 by Division Method

To calculate the LCM of 56 and 84 by the division method, we will divide the numbers(56, 84) by their prime factors (preferably common). The product of these divisors gives the LCM of 56 and 84.

• Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 56 and 84. Write this prime number(2) on the left of the given numbers(56 and 84), separated as per the ladder arrangement.
• Step 2: If any of the given numbers (56, 84) 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 56 and 84 is the product of all prime numbers on the left, i.e. LCM(56, 84) by division method = 2 × 2 × 2 × 3 × 7 = 168.

LCM of 56 and 84 by Listing Multiples

To calculate the LCM of 56 and 84 by listing out the common multiples, we can follow the given below steps:

• Step 1: List a few multiples of 56 (56, 112, 168, 224, 280, . . . ) and 84 (84, 168, 252, 336, 420, 504, . . . . )
• Step 2: The common multiples from the multiples of 56 and 84 are 168, 336, . . .
• Step 3: The smallest common multiple of 56 and 84 is 168.

∴ The least common multiple of 56 and 84 = 168.

LCM of 56 and 84 by Prime Factorization

Prime factorization of 56 and 84 is (2 × 2 × 2 × 7) = 2³ × 7¹ and (2 × 2 × 3 × 7) = 2² × 3¹ × 7¹ respectively. LCM of 56 and 84 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2³ × 3¹ × 7¹ = 168.
Hence, the LCM of 56 and 84 by prime factorization is 168.

☛ Also Check:

• LCM of 5, 9 and 15 - 45
• LCM of 28 and 30 - 420
• LCM of 1 and 2 - 2
• LCM of 24 and 45 - 360
• LCM of 24, 36 and 40 - 360
• LCM of 18, 24 and 30 - 360
• LCM of 4, 8 and 16 - 16

FAQs on LCM of 56 and 84

What is the LCM of 56 and 84?

The LCM of 56 and 84 is 168. To find the LCM of 56 and 84, we need to find the multiples of 56 and 84 (multiples of 56 = 56, 112, 168, 224; multiples of 84 = 84, 168, 252, 336) and choose the smallest multiple that is exactly divisible by 56 and 84, i.e., 168.

How to Find the LCM of 56 and 84 by Prime Factorization?

To find the LCM of 56 and 84 using prime factorization, we will find the prime factors, (56 = 2 × 2 × 2 × 7) and (84 = 2 × 2 × 3 × 7). LCM of 56 and 84 is the product of prime factors raised to their respective highest exponent among the numbers 56 and 84.
⇒ LCM of 56, 84 = 2³ × 3¹ × 7¹ = 168.

Which of the following is the LCM of 56 and 84? 28, 24, 168, 27

The value of LCM of 56, 84 is the smallest common multiple of 56 and 84. The number satisfying the given condition is 168.

What is the Least Perfect Square Divisible by 56 and 84?

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

If the LCM of 84 and 56 is 168, Find its GCF.

LCM(84, 56) × GCF(84, 56) = 84 × 56
Since the LCM of 84 and 56 = 168
⇒ 168 × GCF(84, 56) = 4704
Therefore, the greatest common factor (GCF) = 4704/168 = 28.