LCM of 360, 493, 406, 507
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 360, 493, 406, 507 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 360, 493, 406, 507. So, keep reading to learn more.
Given numbers are 360,493,406,507
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 360,493,406,507 is 209958840.
Find LCM of 360,493,406,507 with Prime Factorization
| 2 | 360, 493, 406, 507 |
| 3 | 180, 493, 203, 507 |
| 29 | 60, 493, 203, 169 |
| 60, 17, 7, 169 |
Multiply the prime numbers at the bottom and the left side.
2 x 3 x 29 x 60 x 17 x 7 x 169 = 209958840
Therefore, the lowest common multiple of 360,493,406,507 is 209958840.
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.
360 x 493 x 406 x 507 = 36532838160
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.
360 : 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180, 360
493 : 1, 17, 29, 493
406 : 1, 2, 7, 14, 29, 58, 203, 406
507 : 1, 3, 13, 39, 169, 507
1 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 360,493,406,507, is 1.
Now, the common factors can be found like this.
360:2x 2x 2x 3x 3x 5
493:17x 29
406:2x 7x 29
507:3x 13x 13
From this, we can see that the common factors because they appear for more than two numbers. So, just multiply them all together.
2x 3x 29 = 174
Therefore, the value for common factors is 174.
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 = 36532838160/(1x174)
LCM = 36532838160/174
LCM = 209958840
Thus, we can understand that the LCM of 360,493,406,507 is 209958840.
LCM of two or more Numbers Calculation Examples
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FAQs on LCM of 360, 493, 406, 507
1. What is the LCM of 360, 493, 406, 507?
Answer: LCM of 360, 493, 406, 507 is 209958840.
2. How to calculate the LCM of 360, 493, 406, 507?
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 360, 493, 406, 507.
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}.