LCM of 16 and 56

LCM of 16 and 56 is the smallest number among all common multiples of 16 and 56. The first few multiples of 16 and 56 are (16, 32, 48, 64, 80, 96, 112, . . . ) and (56, 112, 168, 224, 280, 336, . . . ) respectively. There are 3 commonly used methods to find LCM of 16 and 56 - by prime factorization, by division method, and by listing multiples.

Answer: LCM of 16 and 56 is 112.

Explanation:

The LCM of two non-zero integers, x(16) and y(56), is the smallest positive integer m(112) that is divisible by both x(16) and y(56) without any remainder.

Let's look at the different methods for finding the LCM of 16 and 56.

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

LCM of 16 and 56 by Prime Factorization

Prime factorization of 16 and 56 is (2 × 2 × 2 × 2) = 2⁴ and (2 × 2 × 2 × 7) = 2³ × 7¹ respectively. LCM of 16 and 56 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2⁴ × 7¹ = 112.
Hence, the LCM of 16 and 56 by prime factorization is 112.

LCM of 16 and 56 by Listing Multiples

To calculate the LCM of 16 and 56 by listing out the common multiples, we can follow the given below steps:

• Step 1: List a few multiples of 16 (16, 32, 48, 64, 80, 96, 112, . . . ) and 56 (56, 112, 168, 224, 280, 336, . . . . )
• Step 2: The common multiples from the multiples of 16 and 56 are 112, 224, . . .
• Step 3: The smallest common multiple of 16 and 56 is 112.

∴ The least common multiple of 16 and 56 = 112.

LCM of 16 and 56 by Division Method

To calculate the LCM of 16 and 56 by the division method, we will divide the numbers(16, 56) by their prime factors (preferably common). The product of these divisors gives the LCM of 16 and 56.

• Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 16 and 56. Write this prime number(2) on the left of the given numbers(16 and 56), separated as per the ladder arrangement.
• Step 2: If any of the given numbers (16, 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 16 and 56 is the product of all prime numbers on the left, i.e. LCM(16, 56) by division method = 2 × 2 × 2 × 2 × 7 = 112.

☛ Also Check:

• LCM of 16 and 32 - 32
• LCM of 10 and 25 - 50
• LCM of 3, 4 and 7 - 84
• LCM of 7 and 8 - 56
• LCM of 2, 3 and 5 - 30
• LCM of 11 and 12 - 132
• LCM of 16, 28, 40 and 77 - 6160

FAQs on LCM of 16 and 56

What is the LCM of 16 and 56?

The LCM of 16 and 56 is 112. To find the least common multiple (LCM) of 16 and 56, we need to find the multiples of 16 and 56 (multiples of 16 = 16, 32, 48, 64 . . . . 112; multiples of 56 = 56, 112, 168, 224) and choose the smallest multiple that is exactly divisible by 16 and 56, i.e., 112.

What is the Least Perfect Square Divisible by 16 and 56?

The least number divisible by 16 and 56 = LCM(16, 56)
LCM of 16 and 56 = 2 × 2 × 2 × 2 × 7 [Incomplete pair(s): 7]
⇒ Least perfect square divisible by each 16 and 56 = LCM(16, 56) × 7 = 784 [Square root of 784 = √784 = ±28]
Therefore, 784 is the required number.

If the LCM of 56 and 16 is 112, Find its GCF.

LCM(56, 16) × GCF(56, 16) = 56 × 16
Since the LCM of 56 and 16 = 112
⇒ 112 × GCF(56, 16) = 896
Therefore, the greatest common factor (GCF) = 896/112 = 8.

What is the Relation Between GCF and LCM of 16, 56?

The following equation can be used to express the relation between GCF and LCM of 16 and 56, i.e. GCF × LCM = 16 × 56.

What are the Methods to Find LCM of 16 and 56?

The commonly used methods to find the LCM of 16 and 56 are:

• Division Method
• Listing Multiples
• Prime Factorization Method