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LCM of 614, 126, 180, 106, 540

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


Find the LCM of 614, 126, 180, 106, 540 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 614, 126, 180, 106, 540. So, keep reading to learn more.

 

LCM of:

Calculate the LCM of 614,126,180,106,540

Given numbers are 614,126,180,106,540

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

The LCM of 614,126,180,106,540 is 61504380.

Find LCM of 614,126,180,106,540 with Prime Factorization


2 614, 126, 180, 106, 540
2 307, 63, 90, 53, 270
3 307, 63, 45, 53, 135
3 307, 21, 15, 53, 45
5 307, 7, 5, 53, 15
307, 7, 1, 53, 3

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

2 x 2 x 3 x 3 x 5 x 307 x 7 x 1 x 53 x 3 = 61504380

Therefore, the lowest common multiple of 614,126,180,106,540 is 61504380.

LCM Formula to Find Lowest Common Multiple of 614,126,180,106,540

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.

614 x 126 x 180 x 106 x 540 = 797096764800

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.

614 : 1, 2, 307, 614

126 : 1, 2, 3, 6, 7, 9, 14, 18, 21, 42, 63, 126

180 : 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, 180

106 : 1, 2, 53, 106

540 : 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 27, 30, 36, 45, 54, 60, 90, 108, 135, 180, 270, 540

2 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 614,126,180,106,540, is 2.

Now, the common factors can be found like this.

614:2x 307

126:2x 3x 3x 7

180:2x 2x 3x 3x 5

106:2x 53

540:2x 2x 3x 3x 3x 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 2x 2x 3x 3x 3x 3x 5 = 6480

Therefore, the value for common factors is 6480.

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 = 797096764800/(2x6480)

LCM = 797096764800/12960

LCM = 61504380

Thus, we can understand that the LCM of 614,126,180,106,540 is 61504380.

LCM of two or more Numbers Calculation Examples

FAQs on LCM of 614, 126, 180, 106, 540

1. What is the LCM of 614, 126, 180, 106, 540?

Answer: LCM of 614, 126, 180, 106, 540 is 61504380.

2. How to calculate the LCM of 614, 126, 180, 106, 540?

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 614, 126, 180, 106, 540.

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}.