LCM of 732, 678, 460, 462, 742
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 732, 678, 460, 462, 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 732, 678, 460, 462, 742. So, keep reading to learn more.
Given numbers are 732,678,460,462,742
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 732,678,460,462,742 is 38819859540.
Find LCM of 732,678,460,462,742 with Prime Factorization
| 2 | 732, 678, 460, 462, 742 |
| 2 | 366, 339, 230, 231, 371 |
| 3 | 183, 339, 115, 231, 371 |
| 7 | 61, 113, 115, 77, 371 |
| 61, 113, 115, 11, 53 |
Multiply the prime numbers at the bottom and the left side.
2 x 2 x 3 x 7 x 61 x 113 x 115 x 11 x 53 = 38819859540
Therefore, the lowest common multiple of 732,678,460,462,742 is 38819859540.
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.
732 x 678 x 460 x 462 x 742 = 78260836832640
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.
732 : 1, 2, 3, 4, 6, 12, 61, 122, 183, 244, 366, 732
678 : 1, 2, 3, 6, 113, 226, 339, 678
460 : 1, 2, 4, 5, 10, 20, 23, 46, 92, 115, 230, 460
462 : 1, 2, 3, 6, 7, 11, 14, 21, 22, 33, 42, 66, 77, 154, 231, 462
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 732,678,460,462,742, is 2.
Now, the common factors can be found like this.
732:2x 2x 3x 61
678:2x 3x 113
460:2x 2x 5x 23
462:2x 3x 7x 11
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 3x 3x 7 = 1008
Therefore, the value for common factors is 1008.
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 = 78260836832640/(2x1008)
LCM = 78260836832640/2016
LCM = 38819859540
Thus, we can understand that the LCM of 732,678,460,462,742 is 38819859540.
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FAQs on LCM of 732, 678, 460, 462, 742
1. What is the LCM of 732, 678, 460, 462, 742?
Answer: LCM of 732, 678, 460, 462, 742 is 38819859540.
2. How to calculate the LCM of 732, 678, 460, 462, 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 732, 678, 460, 462, 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}.