LCM of 403, 420, 735, 646, 840
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 403, 420, 735, 646, 840 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 403, 420, 735, 646, 840. So, keep reading to learn more.
Given numbers are 403,420,735,646,840
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 403,420,735,646,840 is 765393720.
Find LCM of 403,420,735,646,840 with Prime Factorization
| 2 | 403, 420, 735, 646, 840 |
| 2 | 403, 210, 735, 323, 420 |
| 3 | 403, 105, 735, 323, 210 |
| 5 | 403, 35, 245, 323, 70 |
| 7 | 403, 7, 49, 323, 14 |
| 403, 1, 7, 323, 2 |
Multiply the prime numbers at the bottom and the left side.
2 x 2 x 3 x 5 x 7 x 403 x 1 x 7 x 323 x 2 = 765393720
Therefore, the lowest common multiple of 403,420,735,646,840 is 765393720.
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.
403 x 420 x 735 x 646 x 840 = 67507726104000
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.
403 : 1, 13, 31, 403
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
646 : 1, 2, 17, 19, 34, 38, 323, 646
840 : 1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 20, 21, 24, 28, 30, 35, 40, 42, 56, 60, 70, 84, 105, 120, 140, 168, 210, 280, 420, 840
1 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 403,420,735,646,840, is 1.
Now, the common factors can be found like this.
403:13x 31
420:2x 2x 3x 5x 7
735:3x 5x 7x 7
646:2x 17x 19
840:2x 2x 2x 3x 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 3x 3x 5x 5x 7x 7 = 88200
Therefore, the value for common factors is 88200.
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 = 67507726104000/(1x88200)
LCM = 67507726104000/88200
LCM = 765393720
Thus, we can understand that the LCM of 403,420,735,646,840 is 765393720.
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FAQs on LCM of 403, 420, 735, 646, 840
1. What is the LCM of 403, 420, 735, 646, 840?
Answer: LCM of 403, 420, 735, 646, 840 is 765393720.
2. How to calculate the LCM of 403, 420, 735, 646, 840?
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 403, 420, 735, 646, 840.
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}.