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LCM of 465, 420, 735, 834

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


Find the LCM of 465, 420, 735, 834 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 465, 420, 735, 834. So, keep reading to learn more.

 

LCM of:

Calculate the LCM of 465,420,735,834

Given numbers are 465,420,735,834

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

The LCM of 465,420,735,834 is 12668460.

Find LCM of 465,420,735,834 with Prime Factorization


2 465, 420, 735, 834
3 465, 210, 735, 417
5 155, 70, 245, 139
7 31, 14, 49, 139
31, 2, 7, 139

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

2 x 3 x 5 x 7 x 31 x 2 x 7 x 139 = 12668460

Therefore, the lowest common multiple of 465,420,735,834 is 12668460.

LCM Formula to Find Lowest Common Multiple of 465,420,735,834

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.

465 x 420 x 735 x 834 = 119716947000

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.

465 : 1, 3, 5, 15, 31, 93, 155, 465

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

735 : 1, 3, 5, 7, 15, 21, 35, 49, 105, 147, 245, 735

834 : 1, 2, 3, 6, 139, 278, 417, 834

3 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 465,420,735,834, is 3.

Now, the common factors can be found like this.

465:3x 5x 31

420:2x 2x 3x 5x 7

735:3x 5x 7x 7

834:2x 3x 139

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

2x 3x 3x 5x 5x 7 = 3150

Therefore, the value for common factors is 3150.

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 = 119716947000/(3x3150)

LCM = 119716947000/9450

LCM = 12668460

Thus, we can understand that the LCM of 465,420,735,834 is 12668460.

LCM of two or more Numbers Calculation Examples

FAQs on LCM of 465, 420, 735, 834

1. What is the LCM of 465, 420, 735, 834?

Answer: LCM of 465, 420, 735, 834 is 12668460.

2. How to calculate the LCM of 465, 420, 735, 834?

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 465, 420, 735, 834.

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}.