LCM of 756, 748, 840, 900
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 756, 748, 840, 900 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 756, 748, 840, 900. So, keep reading to learn more.
Given numbers are 756,748,840,900
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 756,748,840,900 is 7068600.
Find LCM of 756,748,840,900 with Prime Factorization
| 2 | 756, 748, 840, 900 |
| 2 | 378, 374, 420, 450 |
| 3 | 189, 187, 210, 225 |
| 3 | 63, 187, 70, 75 |
| 5 | 21, 187, 70, 25 |
| 7 | 21, 187, 14, 5 |
| 3, 187, 2, 5 |
Multiply the prime numbers at the bottom and the left side.
2 x 2 x 3 x 3 x 5 x 7 x 3 x 187 x 2 x 5 = 7068600
Therefore, the lowest common multiple of 756,748,840,900 is 7068600.
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.
756 x 748 x 840 x 900 = 427508928000
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.
756 : 1, 2, 3, 4, 6, 7, 9, 12, 14, 18, 21, 27, 28, 36, 42, 54, 63, 84, 108, 126, 189, 252, 378, 756
748 : 1, 2, 4, 11, 17, 22, 34, 44, 68, 187, 374, 748
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
900 : 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 25, 30, 36, 45, 50, 60, 75, 90, 100, 150, 180, 225, 300, 450, 900
4 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 756,748,840,900, is 4.
Now, the common factors can be found like this.
756:2x 2x 3x 3x 3x 7
748:2x 2x 11x 17
840:2x 2x 2x 3x 5x 7
900:2x 2x 3x 3x 5x 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 5x 7 = 15120
Therefore, the value for common factors is 15120.
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 = 427508928000/(4x15120)
LCM = 427508928000/60480
LCM = 7068600
Thus, we can understand that the LCM of 756,748,840,900 is 7068600.
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FAQs on LCM of 756, 748, 840, 900
1. What is the LCM of 756, 748, 840, 900?
Answer: LCM of 756, 748, 840, 900 is 7068600.
2. How to calculate the LCM of 756, 748, 840, 900?
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 756, 748, 840, 900.
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}.