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114 Learners

Last updated on ** September 13th, 2024**

The Least common multiple (LCM) is the smallest number that is divisible by the numbers 6 and 8. The LCM can be found using the listing multiples method, the prime factorization and/or division methods. LCM helps to solve problems with fractions and scenarios like scheduling or aligning repeating cycle of events.

The LCM of 6 and 8 is the smallest positive integer, a multiple of both numbers. By finding the LCM, we can simplify the arithmetic operations with fractions to equate the denominators.

There are various methods to find the LCM, Listing method, prime factorization method and division method are explained below;

The LCM of 6 and 8 can be found using the following steps:

**Steps**

1. Write down the multiples of each number:

Multiples of 6 = 6,12,18,24…

Multiples of 8 = 8,16,24,...

2. Ascertain the smallest multiple from the listed multiples

The least common multiple of the numbers is 24.

The prime factors of each number are written, and then the highest power of the prime factors is multiplied to get the LCM.

**Steps:**

1. Find the prime factors of the numbers:

Prime factorization of 6 = 2×3

Prime factorization of 8 = 2×2×2

2. Take the highest power of each prime factor and multiply the highest power of each factor to get the LCM;

— 2,2,3,2

LCM (6,8) = 24

The Division Method involves simultaneously dividing the numbers by their prime factors and multiplying the divisors to get the LCM.

**Steps:**

1. Write down the numbers in a row;

2. Divide the row of numbers by a prime number that is evenly divisible into at least one of the given numbers.

3. Continue dividing the numbers until the last row of the results is ‘1’ and bring down the numbers not divisible by the previously chosen prime number.

4. The LCM of the numbers is the product of the prime numbers in the first column, i.e,

2×2×2×3 = 24

**Multiple:**A number and any integer multiplied.

**Prime Factor:**A natural number (other than 1) that has factors that are one and itself.

**Prime Factorization:**The process of breaking down a number into its prime factors is called Prime Factorization.

**Co-prime numbers:**When the only positive integer that is a divisor of them both is 1, a number is co-prime.

**Relatively Prime Numbers:**Numbers that have no common factors other than 1.

**Fraction:**A representation of a part of a whole.