LCM of 16 and 28

LCM of 16 and 28 is the smallest number among all common multiples of 16 and 28. The first few multiples of 16 and 28 are (16, 32, 48, 64, . . . ) and (28, 56, 84, 112, . . . ) respectively. There are 3 commonly used methods to find LCM of 16 and 28 - by listing multiples, by division method, and by prime factorization.

Answer: LCM of 16 and 28 is 112.

Explanation:

The LCM of two non-zero integers, x(16) and y(28), is the smallest positive integer m(112) that is divisible by both x(16) and y(28) without any remainder.

The methods to find the LCM of 16 and 28 are explained below.

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

LCM of 16 and 28 by Listing Multiples

To calculate the LCM of 16 and 28 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, . . . ) and 28 (28, 56, 84, 112, . . . . )
• Step 2: The common multiples from the multiples of 16 and 28 are 112, 224, . . .
• Step 3: The smallest common multiple of 16 and 28 is 112.

∴ The least common multiple of 16 and 28 = 112.

LCM of 16 and 28 by Prime Factorization

Prime factorization of 16 and 28 is (2 × 2 × 2 × 2) = 2⁴ and (2 × 2 × 7) = 2² × 7¹ respectively. LCM of 16 and 28 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2⁴ × 7¹ = 112.
Hence, the LCM of 16 and 28 by prime factorization is 112.

LCM of 16 and 28 by Division Method

To calculate the LCM of 16 and 28 by the division method, we will divide the numbers(16, 28) by their prime factors (preferably common). The product of these divisors gives the LCM of 16 and 28.

• Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 16 and 28. Write this prime number(2) on the left of the given numbers(16 and 28), separated as per the ladder arrangement.
• Step 2: If any of the given numbers (16, 28) 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 28 is the product of all prime numbers on the left, i.e. LCM(16, 28) by division method = 2 × 2 × 2 × 2 × 7 = 112.

☛ Also Check:

• LCM of 5 and 30 - 30
• LCM of 3, 5 and 8 - 120
• LCM of 1 and 2 - 2
• LCM of 9 and 24 - 72
• LCM of 9 and 30 - 90
• LCM of 45 and 54 - 270
• LCM of 8, 12 and 16 - 48

FAQs on LCM of 16 and 28

What is the LCM of 16 and 28?

The LCM of 16 and 28 is 112. To find the LCM of 16 and 28, we need to find the multiples of 16 and 28 (multiples of 16 = 16, 32, 48, 64 . . . . 112; multiples of 28 = 28, 56, 84, 112) and choose the smallest multiple that is exactly divisible by 16 and 28, i.e., 112.

Which of the following is the LCM of 16 and 28? 36, 18, 42, 112

The value of LCM of 16, 28 is the smallest common multiple of 16 and 28. The number satisfying the given condition is 112.

If the LCM of 28 and 16 is 112, Find its GCF.

LCM(28, 16) × GCF(28, 16) = 28 × 16
Since the LCM of 28 and 16 = 112
⇒ 112 × GCF(28, 16) = 448
Therefore, the GCF = 448/112 = 4.

What is the Relation Between GCF and LCM of 16, 28?

The following equation can be used to express the relation between GCF and LCM of 16 and 28, i.e. GCF × LCM = 16 × 28.

What are the Methods to Find LCM of 16 and 28?

The commonly used methods to find the LCM of 16 and 28 are:

• Prime Factorization Method
• Listing Multiples
• Division Method