LCM of 340, 638, 378, 420, 506
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 340, 638, 378, 420, 506 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 340, 638, 378, 420, 506. So, keep reading to learn more.
Given numbers are 340,638,378,420,506
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 340,638,378,420,506 is 471475620.
Find LCM of 340,638,378,420,506 with Prime Factorization
| 2 | 340, 638, 378, 420, 506 |
| 2 | 170, 319, 189, 210, 253 |
| 3 | 85, 319, 189, 105, 253 |
| 5 | 85, 319, 63, 35, 253 |
| 7 | 17, 319, 63, 7, 253 |
| 11 | 17, 319, 9, 1, 253 |
| 17, 29, 9, 1, 23 |
Multiply the prime numbers at the bottom and the left side.
2 x 2 x 3 x 5 x 7 x 11 x 17 x 29 x 9 x 1 x 23 = 471475620
Therefore, the lowest common multiple of 340,638,378,420,506 is 471475620.
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.
340 x 638 x 378 x 420 x 506 = 17425738915200
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.
340 : 1, 2, 4, 5, 10, 17, 20, 34, 68, 85, 170, 340
638 : 1, 2, 11, 22, 29, 58, 319, 638
378 : 1, 2, 3, 6, 7, 9, 14, 18, 21, 27, 42, 54, 63, 126, 189, 378
420 : 1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 28, 30, 35, 42, 60, 70, 84, 105, 140, 210, 420
506 : 1, 2, 11, 22, 23, 46, 253, 506
2 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 340,638,378,420,506, is 2.
Now, the common factors can be found like this.
340:2x 2x 5x 17
638:2x 11x 29
378:2x 3x 3x 3x 7
420:2x 2x 3x 5x 7
506:2x 11x 23
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 5x 7x 11 = 18480
Therefore, the value for common factors is 18480.
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 = 17425738915200/(2x18480)
LCM = 17425738915200/36960
LCM = 471475620
Thus, we can understand that the LCM of 340,638,378,420,506 is 471475620.
LCM of two or more Numbers Calculation Examples
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FAQs on LCM of 340, 638, 378, 420, 506
1. What is the LCM of 340, 638, 378, 420, 506?
Answer: LCM of 340, 638, 378, 420, 506 is 471475620.
2. How to calculate the LCM of 340, 638, 378, 420, 506?
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 340, 638, 378, 420, 506.
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}.