LCM of 7 and 56

LCM of 7 and 56 is the smallest number among all common multiples of 7 and 56. The first few multiples of 7 and 56 are (7, 14, 21, 28, 35, 42, 49, . . . ) and (56, 112, 168, 224, . . . ) respectively. There are 3 commonly used methods to find LCM of 7 and 56 - by listing multiples, by prime factorization, and by division method.

Answer: LCM of 7 and 56 is 56.

Explanation:

The LCM of two non-zero integers, x(7) and y(56), is the smallest positive integer m(56) that is divisible by both x(7) and y(56) without any remainder.

The methods to find the LCM of 7 and 56 are explained below.

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

LCM of 7 and 56 by Division Method

To calculate the LCM of 7 and 56 by the division method, we will divide the numbers(7, 56) by their prime factors (preferably common). The product of these divisors gives the LCM of 7 and 56.

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

LCM of 7 and 56 by Listing Multiples

To calculate the LCM of 7 and 56 by listing out the common multiples, we can follow the given below steps:

• Step 1: List a few multiples of 7 (7, 14, 21, 28, 35, 42, 49, . . . ) and 56 (56, 112, 168, 224, . . . . )
• Step 2: The common multiples from the multiples of 7 and 56 are 56, 112, . . .
• Step 3: The smallest common multiple of 7 and 56 is 56.

∴ The least common multiple of 7 and 56 = 56.

LCM of 7 and 56 by Prime Factorization

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

☛ Also Check:

• LCM of 3, 5 and 7 - 105
• LCM of 30, 72 and 432 - 2160
• LCM of 8 and 11 - 88
• LCM of 7, 8, 11 and 12 - 1848
• LCM of 36 and 42 - 252
• LCM of 5, 10, 15 and 30 - 30
• LCM of 9 and 13 - 117

FAQs on LCM of 7 and 56

What is the LCM of 7 and 56?

The LCM of 7 and 56 is 56. To find the LCM (least common multiple) of 7 and 56, we need to find the multiples of 7 and 56 (multiples of 7 = 7, 14, 21, 28 . . . . 56; multiples of 56 = 56, 112, 168, 224) and choose the smallest multiple that is exactly divisible by 7 and 56, i.e., 56.

If the LCM of 56 and 7 is 56, Find its GCF.

LCM(56, 7) × GCF(56, 7) = 56 × 7
Since the LCM of 56 and 7 = 56
⇒ 56 × GCF(56, 7) = 392
Therefore, the GCF = 392/56 = 7.

What are the Methods to Find LCM of 7 and 56?

The commonly used methods to find the LCM of 7 and 56 are:

• Listing Multiples
• Division Method
• Prime Factorization Method

What is the Relation Between GCF and LCM of 7, 56?

The following equation can be used to express the relation between GCF and LCM of 7 and 56, i.e. GCF × LCM = 7 × 56.

What is the Least Perfect Square Divisible by 7 and 56?

The least number divisible by 7 and 56 = LCM(7, 56)
LCM of 7 and 56 = 2 × 2 × 2 × 7 [Incomplete pair(s): 2, 7]
⇒ Least perfect square divisible by each 7 and 56 = LCM(7, 56) × 2 × 7 = 784 [Square root of 784 = √784 = ±28]
Therefore, 784 is the required number.