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LCM of 420, 665, 300

Created By : Jatin Gogia
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023


Find the LCM of 420, 665, 300 with the LCM of Two or More Numbers Calculator. Here we are teaching you two different methods through which you can calculate the LCM of 420, 665, 300. So, keep reading to learn more.

 

LCM of:

Calculate the LCM of 420,665,300

Given numbers are 420,665,300

The least common multiple of numbers can be find using the prime factorization method or LCM formula.

The LCM of 420,665,300 is 39900.

Find LCM of 420,665,300 with Prime Factorization


2 420, 665, 300
2 210, 665, 150
3 105, 665, 75
5 35, 665, 25
7 7, 133, 5
1, 19, 5

Multiply the prime numbers at the bottom and the left side.

2 x 2 x 3 x 5 x 7 x 1 x 19 x 5 = 39900

Therefore, the lowest common multiple of 420,665,300 is 39900.

LCM Formula to Find Lowest Common Multiple of 420,665,300

LCM formula is LCM(a1, a2, an) = (a1 x a2 x an)/{GCF(a1 x a2 x an) x common factors}

Firstly, we have to find the product of all the numbers.

420 x 665 x 300 = 83790000

Then, let us find the GCF of these five numbers. To do so, we have to list down the factors for each number and choose the highest factor that is in all of the lists.

420 : 1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 28, 30, 35, 42, 60, 70, 84, 105, 140, 210, 420

665 : 1, 5, 7, 19, 35, 95, 133, 665

300 : 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 60, 75, 100, 150, 300

5 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 420,665,300, is 5.

Now, the common factors can be found like this.

420:2x 2x 3x 5x 7

665:5x 7x 19

300:2x 2x 3x 5x 5

From this, we can see that the common factors because they appear for more than two numbers. So, just multiply them all together.

2x 2x 3x 5x 7 = 420

Therefore, the value for common factors is 420.

Now that we have all the elements of the formula, we can plug them in to calculate the LCM.

LCM(a1, a2, an) = (a1 x a2 x an)/{GCF(a1 x a2 x an) x common factors}

LCM = 83790000/(5x420)

LCM = 83790000/2100

LCM = 39900

Thus, we can understand that the LCM of 420,665,300 is 39900.

LCM of two or more Numbers Calculation Examples

Here are some samples of LCM of two or more Numbers calculations.

FAQs on LCM of 420, 665, 300

1. What is the LCM of 420, 665, 300?

Answer: LCM of 420, 665, 300 is 39900.

2. How to calculate the LCM of 420, 665, 300?

The LCM can be found using two methods. You can either use the LCM formula or the prime factorization method to calculate the LCM of 420, 665, 300.

3. What is the LCM formula?

The LCM formula is LCM(a1, a2, an) = (a1 x a2 x an)/{GCF(a1 x a2 x an) x common factors}.