Welcome to our blog on the least common multiple (LCM) of 10 and 12 In this blog, we will be diving into the different methods for finding the LCM, including the prime factorization method, the listing multiples method, and the division method. Learn how to find the LCM and make your life a little bit easier in scheduling or managing time.

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## LCM of 10 and 12

The least common multiple (LCM) of two numbers is the smallest number that is a multiple of both numbers. To find the LCM of 10 and 12, you can list out the multiples of each number and look for the smallest one that they have in common.

A more efficient method is to use the formula for the LCM, which is:

LCM(a,b) = (a x b) / GCD(a,b)

Where GCD is the greatest common divisor of a and b.

In this case, GCD of 10 and 12 is 2

so, LCM(10,12) = (10 x 12) / 2 = 60

Hence, LCM of 10 and 12 is 60

## LCM of 10 and 12 though Listing Multiples

The method of listing multiples to find the LCM of two numbers involves listing out the multiples of each number and looking for the smallest one that they have in common.

Multiples of 10: 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120, 130, 140, 150, …

Multiples of 12: 12, 24, 36, 48, 60, 72, 84, 96, 108, 120, 132, 144, 156, 168, 180, …

As we can see the smallest common multiple of 10 and 12 is 60, which is the LCM of 10 and 12.

Hence, LCM of 10 and 12 by Listing Multiples method is 60.

## LCM of 10 and 12 by Prime Factorization

The prime factorization method for finding the LCM of two numbers involves breaking down each number into its prime factors, then multiplying the highest powers of each prime factor together.

To find the prime factorization of 10, we can start by dividing it by the smallest prime number, 2.

10 / 2 = 5

5 is a prime number, so the prime factorization of 10 is 2 * 5

To find the prime factorization of 12, we can start by dividing it by the smallest prime number, 2.

12 / 2 = 6

6 is not a prime number, it can be further divided by 2 to get 3.

so the prime factorization of 12 is 2^2 * 3

To find the LCM, we take the highest powers of each prime factor and multiply them together.

LCM(10, 12) = (2^2) * (3^1) * (5^1)

= 4 * 3 * 5

= 60

Hence, LCM of 10 and 12 by Prime Factorization method is 60.

## LCM of 10 and 12 by Division Method

The division method for finding the LCM of two numbers involves dividing the product of the two numbers by their greatest common divisor (GCD).

The steps to find the LCM of two numbers using the division method are:

Multiply the two numbers together, in this case 10 x 12 = 120

Find the GCD of the two numbers, in this case GCD(10,12) = 2

Divide the product of the two numbers by the GCD.

LCM = (10 x 12) / GCD(10,12) = 120/2 = 60

Hence, LCM of 10 and 12 by Division Method is 60

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