LCM of 8 and 28

LCM of 8 and 28 is the smallest number among all common multiples of 8 and 28. The first few multiples of 8 and 28 are (8, 16, 24, 32, 40, 48, . . . ) and (28, 56, 84, 112, 140, 168, . . . ) respectively. There are 3 commonly used methods to find LCM of 8 and 28 - by prime factorization, by division method, and by listing multiples.

Answer: LCM of 8 and 28 is 56.

Explanation:

The LCM of two non-zero integers, x(8) and y(28), is the smallest positive integer m(56) that is divisible by both x(8) and y(28) without any remainder.

Let's look at the different methods for finding the LCM of 8 and 28.

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

LCM of 8 and 28 by Listing Multiples

To calculate the LCM of 8 and 28 by listing out the common multiples, we can follow the given below steps:

• Step 1: List a few multiples of 8 (8, 16, 24, 32, 40, 48, . . . ) and 28 (28, 56, 84, 112, 140, 168, . . . . )
• Step 2: The common multiples from the multiples of 8 and 28 are 56, 112, . . .
• Step 3: The smallest common multiple of 8 and 28 is 56.

∴ The least common multiple of 8 and 28 = 56.

LCM of 8 and 28 by Division Method

To calculate the LCM of 8 and 28 by the division method, we will divide the numbers(8, 28) by their prime factors (preferably common). The product of these divisors gives the LCM of 8 and 28.

• Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 8 and 28. Write this prime number(2) on the left of the given numbers(8 and 28), separated as per the ladder arrangement.
• Step 2: If any of the given numbers (8, 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 8 and 28 is the product of all prime numbers on the left, i.e. LCM(8, 28) by division method = 2 × 2 × 2 × 7 = 56.

LCM of 8 and 28 by Prime Factorization

Prime factorization of 8 and 28 is (2 × 2 × 2) = 2³ and (2 × 2 × 7) = 2² × 7¹ respectively. LCM of 8 and 28 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2³ × 7¹ = 56.
Hence, the LCM of 8 and 28 by prime factorization is 56.

☛ Also Check:

• LCM of 26 and 91 - 182
• LCM of 45 and 120 - 360
• LCM of 24 and 90 - 360
• LCM of 21 and 56 - 168
• LCM of 3 and 10 - 30
• LCM of 30, 72 and 432 - 2160
• LCM of 20 and 22 - 220

FAQs on LCM of 8 and 28

What is the LCM of 8 and 28?

The LCM of 8 and 28 is 56. To find the LCM (least common multiple) of 8 and 28, we need to find the multiples of 8 and 28 (multiples of 8 = 8, 16, 24, 32 . . . . 56; multiples of 28 = 28, 56, 84, 112) and choose the smallest multiple that is exactly divisible by 8 and 28, i.e., 56.

What is the Least Perfect Square Divisible by 8 and 28?

The least number divisible by 8 and 28 = LCM(8, 28)
LCM of 8 and 28 = 2 × 2 × 2 × 7 [Incomplete pair(s): 2, 7]
⇒ Least perfect square divisible by each 8 and 28 = LCM(8, 28) × 2 × 7 = 784 [Square root of 784 = √784 = ±28]
Therefore, 784 is the required number.

If the LCM of 28 and 8 is 56, Find its GCF.

LCM(28, 8) × GCF(28, 8) = 28 × 8
Since the LCM of 28 and 8 = 56
⇒ 56 × GCF(28, 8) = 224
Therefore, the greatest common factor = 224/56 = 4.

Which of the following is the LCM of 8 and 28? 35, 10, 56, 42

The value of LCM of 8, 28 is the smallest common multiple of 8 and 28. The number satisfying the given condition is 56.

How to Find the LCM of 8 and 28 by Prime Factorization?

To find the LCM of 8 and 28 using prime factorization, we will find the prime factors, (8 = 2 × 2 × 2) and (28 = 2 × 2 × 7). LCM of 8 and 28 is the product of prime factors raised to their respective highest exponent among the numbers 8 and 28.
⇒ LCM of 8, 28 = 2³ × 7¹ = 56.