LCM of 784, 493, 120, 972
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 784, 493, 120, 972 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 784, 493, 120, 972. So, keep reading to learn more.
Given numbers are 784,493,120,972
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 784,493,120,972 is 469612080.
Find LCM of 784,493,120,972 with Prime Factorization
| 2 | 784, 493, 120, 972 |
| 2 | 392, 493, 60, 486 |
| 2 | 196, 493, 30, 243 |
| 3 | 98, 493, 15, 243 |
| 98, 493, 5, 81 |
Multiply the prime numbers at the bottom and the left side.
2 x 2 x 2 x 3 x 98 x 493 x 5 x 81 = 469612080
Therefore, the lowest common multiple of 784,493,120,972 is 469612080.
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.
784 x 493 x 120 x 972 = 45082759680
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.
784 : 1, 2, 4, 7, 8, 14, 16, 28, 49, 56, 98, 112, 196, 392, 784
493 : 1, 17, 29, 493
120 : 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120
972 : 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 81, 108, 162, 243, 324, 486, 972
1 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 784,493,120,972, is 1.
Now, the common factors can be found like this.
784:2x 2x 2x 2x 7x 7
493:17x 29
120:2x 2x 2x 3x 5
972:2x 2x 3x 3x 3x 3x 3
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 3 = 96
Therefore, the value for common factors is 96.
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 = 45082759680/(1x96)
LCM = 45082759680/96
LCM = 469612080
Thus, we can understand that the LCM of 784,493,120,972 is 469612080.
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FAQs on LCM of 784, 493, 120, 972
1. What is the LCM of 784, 493, 120, 972?
Answer: LCM of 784, 493, 120, 972 is 469612080.
2. How to calculate the LCM of 784, 493, 120, 972?
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 784, 493, 120, 972.
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}.