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113 Learners

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

The Least common multiple (LCM) is the smallest number that is divisible by the numbers 6 and 10. 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 10 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;

To ascertain the LCM, list the multiples of the integers until a common multiple is found.

**Steps:**

1. Write down the multiples of each number:

Multiples of 6 = 6,12,18,24,30,…

Multiples of 10 = 10,20,30,40…

2. Ascertain the smallest multiple from the listed multiples

The least common multiple of the numbers is 30.

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 10= 2×5

2. Take the highest power of each prime factor and multiply the ascertained factors.

— 2,3,5 = LCM, i.e, 30

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,

2×5×3 = 30

**Multiple:**A product of a number and any integer.

**Prime Factor:**A prime factor is a natural number, other than 1, whose only factors are 1 and itself.

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

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

**Greatest Common Divisor (GCD):**The largest positive integer that divides each of two or more integers without leaving a remainder.

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

**Fraction:**A number representing a part of a whole.