LCM of 972, 204, 384, 144, 742
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 972, 204, 384, 144, 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 972, 204, 384, 144, 742. So, keep reading to learn more.
Given numbers are 972,204,384,144,742
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 972,204,384,144,742 is 196172928.
Find LCM of 972,204,384,144,742 with Prime Factorization
| 2 | 972, 204, 384, 144, 742 |
| 2 | 486, 102, 192, 72, 371 |
| 2 | 243, 51, 96, 36, 371 |
| 2 | 243, 51, 48, 18, 371 |
| 3 | 243, 51, 24, 9, 371 |
| 3 | 81, 17, 8, 3, 371 |
| 27, 17, 8, 1, 371 |
Multiply the prime numbers at the bottom and the left side.
2 x 2 x 2 x 2 x 3 x 3 x 27 x 17 x 8 x 1 x 371 = 196172928
Therefore, the lowest common multiple of 972,204,384,144,742 is 196172928.
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.
972 x 204 x 384 x 144 x 742 = 8135683670016
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.
972 : 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 81, 108, 162, 243, 324, 486, 972
204 : 1, 2, 3, 4, 6, 12, 17, 34, 51, 68, 102, 204
384 : 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 128, 192, 384
144 : 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144
742 : 1, 2, 7, 14, 53, 106, 371, 742
2 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 972,204,384,144,742, is 2.
Now, the common factors can be found like this.
972:2x 2x 3x 3x 3x 3x 3
204:2x 2x 3x 17
384:2x 2x 2x 2x 2x 2x 2x 3
144:2x 2x 2x 2x 3x 3
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 2x 2x 2x 3x 3x 3x 3 = 20736
Therefore, the value for common factors is 20736.
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 = 8135683670016/(2x20736)
LCM = 8135683670016/41472
LCM = 196172928
Thus, we can understand that the LCM of 972,204,384,144,742 is 196172928.
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FAQs on LCM of 972, 204, 384, 144, 742
1. What is the LCM of 972, 204, 384, 144, 742?
Answer: LCM of 972, 204, 384, 144, 742 is 196172928.
2. How to calculate the LCM of 972, 204, 384, 144, 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 972, 204, 384, 144, 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}.