LCM of 375, 824, 680, 720, 408
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 375, 824, 680, 720, 408 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 375, 824, 680, 720, 408. So, keep reading to learn more.
Given numbers are 375,824,680,720,408
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 375,824,680,720,408 is 31518000.
Find LCM of 375,824,680,720,408 with Prime Factorization
| 2 | 375, 824, 680, 720, 408 |
| 2 | 375, 412, 340, 360, 204 |
| 2 | 375, 206, 170, 180, 102 |
| 3 | 375, 103, 85, 90, 51 |
| 5 | 125, 103, 85, 30, 17 |
| 17 | 25, 103, 17, 6, 17 |
| 25, 103, 1, 6, 1 |
Multiply the prime numbers at the bottom and the left side.
2 x 2 x 2 x 3 x 5 x 17 x 25 x 103 x 1 x 6 x 1 = 31518000
Therefore, the lowest common multiple of 375,824,680,720,408 is 31518000.
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.
375 x 824 x 680 x 720 x 408 = 61724851200000
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.
375 : 1, 3, 5, 15, 25, 75, 125, 375
824 : 1, 2, 4, 8, 103, 206, 412, 824
680 : 1, 2, 4, 5, 8, 10, 17, 20, 34, 40, 68, 85, 136, 170, 340, 680
720 : 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 30, 36, 40, 45, 48, 60, 72, 80, 90, 120, 144, 180, 240, 360, 720
408 : 1, 2, 3, 4, 6, 8, 12, 17, 24, 34, 51, 68, 102, 136, 204, 408
1 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 375,824,680,720,408, is 1.
Now, the common factors can be found like this.
375:3x 5x 5x 5
824:2x 2x 2x 103
680:2x 2x 2x 5x 17
720:2x 2x 2x 2x 3x 3x 5
408:2x 2x 2x 3x 17
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 2x 2x 2x 2x 2x 3x 3x 5x 5x 17 = 1958400
Therefore, the value for common factors is 1958400.
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 = 61724851200000/(1x1958400)
LCM = 61724851200000/1958400
LCM = 31518000
Thus, we can understand that the LCM of 375,824,680,720,408 is 31518000.
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FAQs on LCM of 375, 824, 680, 720, 408
1. What is the LCM of 375, 824, 680, 720, 408?
Answer: LCM of 375, 824, 680, 720, 408 is 31518000.
2. How to calculate the LCM of 375, 824, 680, 720, 408?
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 375, 824, 680, 720, 408.
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}.