LCM of 804, 705, 688, 420, 742
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 804, 705, 688, 420, 742 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 804, 705, 688, 420, 742. So, keep reading to learn more.
Given numbers are 804,705,688,420,742
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 804,705,688,420,742 is 12056639280.
Find LCM of 804,705,688,420,742 with Prime Factorization
| 2 | 804, 705, 688, 420, 742 |
| 2 | 402, 705, 344, 210, 371 |
| 3 | 201, 705, 172, 105, 371 |
| 5 | 67, 235, 172, 35, 371 |
| 7 | 67, 47, 172, 7, 371 |
| 67, 47, 172, 1, 53 |
Multiply the prime numbers at the bottom and the left side.
2 x 2 x 3 x 5 x 7 x 67 x 47 x 172 x 1 x 53 = 12056639280
Therefore, the lowest common multiple of 804,705,688,420,742 is 12056639280.
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.
804 x 705 x 688 x 420 x 742 = 121530923942400
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.
804 : 1, 2, 3, 4, 6, 12, 67, 134, 201, 268, 402, 804
705 : 1, 3, 5, 15, 47, 141, 235, 705
688 : 1, 2, 4, 8, 16, 43, 86, 172, 344, 688
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
742 : 1, 2, 7, 14, 53, 106, 371, 742
1 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 804,705,688,420,742, is 1.
Now, the common factors can be found like this.
804:2x 2x 3x 67
705:3x 5x 47
688:2x 2x 2x 2x 43
420:2x 2x 3x 5x 7
742:2x 7x 53
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 3x 3x 5x 7 = 10080
Therefore, the value for common factors is 10080.
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 = 121530923942400/(1x10080)
LCM = 121530923942400/10080
LCM = 12056639280
Thus, we can understand that the LCM of 804,705,688,420,742 is 12056639280.
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FAQs on LCM of 804, 705, 688, 420, 742
1. What is the LCM of 804, 705, 688, 420, 742?
Answer: LCM of 804, 705, 688, 420, 742 is 12056639280.
2. How to calculate the LCM of 804, 705, 688, 420, 742?
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 804, 705, 688, 420, 742.
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}.