Architecture

# Least Common Multiples Of 6 And 8 (B) 12 And 18, Least Common Multiple Of 6 And 8

LCM of 6 and 8 is the smallest number among all common multiples of 6 and 8. The first few multiples of 6 and 8 are (6, 12, 18, 24, 30, 36, 42, . . . ) and (8, 16, 24, 32, . . . ) respectively. There are 3 commonly used methods to find LCM of 6 and 8 – by prime factorization, by division method, and by listing multiples.

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 1 LCM of 6 and 8 2 List of Methods 3 Solved Examples 4 FAQs

Answer: LCM of 6 and 8 is 24.

Explanation:

The LCM of two non-zero integers, x(6) and y(8), is the smallest positive integer m(24) that is divisible by both x(6) and y(8) without any remainder.

Let's look at the different methods for finding the LCM of 6 and 8.

By Prime Factorization MethodBy Listing MultiplesBy Division Method

### LCM of 6 and 8 by Prime Factorization

Prime factorization of 6 and 8 is (2 × 3) = 21 × 31 and (2 × 2 × 2) = 23 respectively. LCM of 6 and 8 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 23 × 31 = 24.Hence, the LCM of 6 and 8 by prime factorization is 24.

### LCM of 6 and 8 by Listing Multiples

To calculate the LCM of 6 and 8 by listing out the common multiples, we can follow the given below steps:

Step 1: List a few multiples of 6 (6, 12, 18, 24, 30, 36, 42, . . . ) and 8 (8, 16, 24, 32, . . . . )Step 2: The common multiples from the multiples of 6 and 8 are 24, 48, . . .Step 3: The smallest common multiple of 6 and 8 is 24.

∴ The least common multiple of 6 and 8 = 24.

### LCM of 6 and 8 by Division Method

To calculate the LCM of 6 and 8 by the division method, we will divide the numbers(6, 8) by their prime factors (preferably common). The product of these divisors gives the LCM of 6 and 8.

Step 3: Continue the steps until only 1s are left in the last row.

The LCM of 6 and 8 is the product of all prime numbers on the left, i.e. LCM(6, 8) by division method = 2 × 2 × 2 × 3 = 24.

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## FAQs on LCM of 6 and 8

### What is the LCM of 6 and 8?

The LCM of 6 and 8 is 24. To find the least common multiple (LCM) of 6 and 8, we need to find the multiples of 6 and 8 (multiples of 6 = 6, 12, 18, 24; multiples of 8 = 8, 16, 24, 32) and choose the smallest multiple that is exactly divisible by 6 and 8, i.e., 24.

### What is the Least Perfect Square Divisible by 6 and 8?

The least number divisible by 6 and 8 = LCM(6, 8)LCM of 6 and 8 = 2 × 2 × 2 × 3 ⇒ Least perfect square divisible by each 6 and 8 = LCM(6, 8) × 2 × 3 = 144 Therefore, 144 is the required number.

### Which of the following is the LCM of 6 and 8? 15, 42, 24, 28

The value of LCM of 6, 8 is the smallest common multiple of 6 and 8. The number satisfying the given condition is 24.

### If the LCM of 8 and 6 is 24, Find its GCF.

LCM(8, 6) × GCF(8, 6) = 8 × 6Since the LCM of 8 and 6 = 24⇒ 24 × GCF(8, 6) = 48Therefore, the greatest common factor (GCF) = 48/24 = 2.

### How to Find the LCM of 6 and 8 by Prime Factorization?

To find the LCM of 6 and 8 using prime factorization, we will find the prime factors, (6 = 2 × 3) and (8 = 2 × 2 × 2). LCM of 6 and 8 is the product of prime factors raised to their respective highest exponent among the numbers 6 and 8.⇒ LCM of 6, 8 = 23 × 31 = 24.