LCM of 428, 312, 689, 780, 175
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 428, 312, 689, 780, 175 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 428, 312, 689, 780, 175. So, keep reading to learn more.
Given numbers are 428,312,689,780,175
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 428,312,689,780,175 is 309636600.
Find LCM of 428,312,689,780,175 with Prime Factorization
| 2 | 428, 312, 689, 780, 175 |
| 2 | 214, 156, 689, 390, 175 |
| 3 | 107, 78, 689, 195, 175 |
| 5 | 107, 26, 689, 65, 175 |
| 13 | 107, 26, 689, 13, 35 |
| 107, 2, 53, 1, 35 |
Multiply the prime numbers at the bottom and the left side.
2 x 2 x 3 x 5 x 13 x 107 x 2 x 53 x 1 x 35 = 309636600
Therefore, the lowest common multiple of 428,312,689,780,175 is 309636600.
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.
428 x 312 x 689 x 780 x 175 = 12558860496000
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.
428 : 1, 2, 4, 107, 214, 428
312 : 1, 2, 3, 4, 6, 8, 12, 13, 24, 26, 39, 52, 78, 104, 156, 312
689 : 1, 13, 53, 689
780 : 1, 2, 3, 4, 5, 6, 10, 12, 13, 15, 20, 26, 30, 39, 52, 60, 65, 78, 130, 156, 195, 260, 390, 780
175 : 1, 5, 7, 25, 35, 175
1 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 428,312,689,780,175, is 1.
Now, the common factors can be found like this.
428:2x 2x 107
312:2x 2x 2x 3x 13
689:13x 53
780:2x 2x 3x 5x 13
175:5x 5x 7
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 5x 13x 13 = 40560
Therefore, the value for common factors is 40560.
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 = 12558860496000/(1x40560)
LCM = 12558860496000/40560
LCM = 309636600
Thus, we can understand that the LCM of 428,312,689,780,175 is 309636600.
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FAQs on LCM of 428, 312, 689, 780, 175
1. What is the LCM of 428, 312, 689, 780, 175?
Answer: LCM of 428, 312, 689, 780, 175 is 309636600.
2. How to calculate the LCM of 428, 312, 689, 780, 175?
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 428, 312, 689, 780, 175.
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}.