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116 Learners

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

The Least common multiple (LCM) is the smallest number that is divisible by the numbers 4 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 4 and 10 is the smallest positive integer, a multiple of both numbers. By finding the LCM, we can simplify the arithmetic operations like addition and subtraction 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 8 and 10 can be found using the following steps:

**Steps:**

1. Write down the multiples of each number

Multiples of 4 = 4, 8, 12, 16, 20, 24, …

Multiples of 10 = 10, 20, 30, 40, …

2. Ascertain the smallest multiple from the listed multiples

The smallest common multiple is 20. Thus, LCM(4, 10) = 20.

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 each number:

Prime factorization of 4 = 2×2

Prime factorization of 10 =2×5

2. Take the highest powers of each prime factor and multiply the highest powers to get the LCM:

LCM(4, 10) = 2×2×5= 20

This method involves dividing both numbers by their common prime factors until no further division is possible, and then multiplying the divisors to find the LCM.

**Steps:**

1. Write the numbers:

2. Divide by common prime factors

3. Multiply the divisors

So, LCM(4, 10) = 20

**Multiple:**A number multiplied with an integer.

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

**Prime Factorization:**Breaking down a number into its prime factors is called Prime Factorization.

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

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