LCM of 420, 589, 402, 708, 218
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 420, 589, 402, 708, 218 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 420, 589, 402, 708, 218. So, keep reading to learn more.
Given numbers are 420,589,402,708,218
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 420,589,402,708,218 is 106590352260.
Find LCM of 420,589,402,708,218 with Prime Factorization
| 2 | 420, 589, 402, 708, 218 |
| 2 | 210, 589, 201, 354, 109 |
| 3 | 105, 589, 201, 177, 109 |
| 35, 589, 67, 59, 109 |
Multiply the prime numbers at the bottom and the left side.
2 x 2 x 3 x 35 x 589 x 67 x 59 x 109 = 106590352260
Therefore, the lowest common multiple of 420,589,402,708,218 is 106590352260.
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.
420 x 589 x 402 x 708 x 218 = 15349010725440
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.
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
589 : 1, 19, 31, 589
402 : 1, 2, 3, 6, 67, 134, 201, 402
708 : 1, 2, 3, 4, 6, 12, 59, 118, 177, 236, 354, 708
218 : 1, 2, 109, 218
1 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 420,589,402,708,218, is 1.
Now, the common factors can be found like this.
420:2x 2x 3x 5x 7
589:19x 31
402:2x 3x 67
708:2x 2x 3x 59
218:2x 109
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 3 = 144
Therefore, the value for common factors is 144.
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 = 15349010725440/(1x144)
LCM = 15349010725440/144
LCM = 106590352260
Thus, we can understand that the LCM of 420,589,402,708,218 is 106590352260.
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FAQs on LCM of 420, 589, 402, 708, 218
1. What is the LCM of 420, 589, 402, 708, 218?
Answer: LCM of 420, 589, 402, 708, 218 is 106590352260.
2. How to calculate the LCM of 420, 589, 402, 708, 218?
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 420, 589, 402, 708, 218.
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}.