LCM of 5 and 8

LCM of 5 and 8 is the smallest number among all common multiples of 5 and 8. The first few multiples of 5 and 8 are (5, 10, 15, 20, 25, 30, . . . ) and (8, 16, 24, 32, 40, 48, 56, . . . ) respectively. There are 3 commonly used methods to find LCM of 5 and 8 - by prime factorization, by listing multiples, and by division method.

Answer: LCM of 5 and 8 is 40.

Explanation:

The LCM of two non-zero integers, x(5) and y(8), is the smallest positive integer m(40) that is divisible by both x(5) and y(8) without any remainder.

The methods to find the LCM of 5 and 8 are explained below.

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

LCM of 5 and 8 by Prime Factorization

Prime factorization of 5 and 8 is (5) = 5¹ and (2 × 2 × 2) = 2³ respectively. LCM of 5 and 8 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2³ × 5¹ = 40.
Hence, the LCM of 5 and 8 by prime factorization is 40.

LCM of 5 and 8 by Division Method

To calculate the LCM of 5 and 8 by the division method, we will divide the numbers(5, 8) by their prime factors (preferably common). The product of these divisors gives the LCM of 5 and 8.

• Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 5 and 8. Write this prime number(2) on the left of the given numbers(5 and 8), separated as per the ladder arrangement.
• Step 2: If any of the given numbers (5, 8) 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 5 and 8 is the product of all prime numbers on the left, i.e. LCM(5, 8) by division method = 2 × 2 × 2 × 5 = 40.

LCM of 5 and 8 by Listing Multiples

To calculate the LCM of 5 and 8 by listing out the common multiples, we can follow the given below steps:

• Step 1: List a few multiples of 5 (5, 10, 15, 20, 25, 30, . . . ) and 8 (8, 16, 24, 32, 40, 48, 56, . . . . )
• Step 2: The common multiples from the multiples of 5 and 8 are 40, 80, . . .
• Step 3: The smallest common multiple of 5 and 8 is 40.

∴ The least common multiple of 5 and 8 = 40.

☛ Also Check:

• LCM of 2, 5 and 7 - 70
• LCM of 14 and 42 - 42
• LCM of 3 and 8 - 24
• LCM of 18, 24 and 36 - 72
• LCM of 60, 84 and 108 - 3780
• LCM of 10 and 100 - 100
• LCM of 8, 9 and 25 - 1800

FAQs on LCM of 5 and 8

What is the LCM of 5 and 8?

The LCM of 5 and 8 is 40. To find the LCM of 5 and 8, we need to find the multiples of 5 and 8 (multiples of 5 = 5, 10, 15, 20 . . . . 40; multiples of 8 = 8, 16, 24, 32 . . . . 40) and choose the smallest multiple that is exactly divisible by 5 and 8, i.e., 40.

If the LCM of 8 and 5 is 40, Find its GCF.

LCM(8, 5) × GCF(8, 5) = 8 × 5
Since the LCM of 8 and 5 = 40
⇒ 40 × GCF(8, 5) = 40
Therefore, the greatest common factor (GCF) = 40/40 = 1.

What is the Relation Between GCF and LCM of 5, 8?

The following equation can be used to express the relation between GCF and LCM of 5 and 8, i.e. GCF × LCM = 5 × 8.

What is the Least Perfect Square Divisible by 5 and 8?

The least number divisible by 5 and 8 = LCM(5, 8)
LCM of 5 and 8 = 2 × 2 × 2 × 5 [Incomplete pair(s): 2, 5]
⇒ Least perfect square divisible by each 5 and 8 = LCM(5, 8) × 2 × 5 = 400 [Square root of 400 = √400 = ±20]
Therefore, 400 is the required number.

Which of the following is the LCM of 5 and 8? 11, 45, 30, 40

The value of LCM of 5, 8 is the smallest common multiple of 5 and 8. The number satisfying the given condition is 40.