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LCM of 465, 735, 208, 469

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


Find the LCM of 465, 735, 208, 469 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, 735, 208, 469. So, keep reading to learn more.

 

LCM of:

Calculate the LCM of 465,735,208,469

Given numbers are 465,735,208,469

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

The LCM of 465,735,208,469 is 317531760.

Find LCM of 465,735,208,469 with Prime Factorization


3 465, 735, 208, 469
5 155, 245, 208, 469
7 31, 49, 208, 469
31, 7, 208, 67

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

3 x 5 x 7 x 31 x 7 x 208 x 67 = 317531760

Therefore, the lowest common multiple of 465,735,208,469 is 317531760.

LCM Formula to Find Lowest Common Multiple of 465,735,208,469

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 735 x 208 x 469 = 33340834800

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

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

208 : 1, 2, 4, 8, 13, 16, 26, 52, 104, 208

469 : 1, 7, 67, 469

1 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 465,735,208,469, is 1.

Now, the common factors can be found like this.

465:3x 5x 31

735:3x 5x 7x 7

208:2x 2x 2x 2x 13

469:7x 67

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

3x 5x 7 = 105

Therefore, the value for common factors is 105.

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 = 33340834800/(1x105)

LCM = 33340834800/105

LCM = 317531760

Thus, we can understand that the LCM of 465,735,208,469 is 317531760.

LCM of two or more Numbers Calculation Examples

FAQs on LCM of 465, 735, 208, 469

1. What is the LCM of 465, 735, 208, 469?

Answer: LCM of 465, 735, 208, 469 is 317531760.

2. How to calculate the LCM of 465, 735, 208, 469?

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, 735, 208, 469.

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}.