LCM of 489, 630, 420
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 489, 630, 420 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 489, 630, 420. So, keep reading to learn more.
Given numbers are 489,630,420
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 489,630,420 is 205380.
Find LCM of 489,630,420 with Prime Factorization
| 2 | 489, 630, 420 |
| 3 | 489, 315, 210 |
| 5 | 163, 105, 70 |
| 7 | 163, 21, 14 |
| 163, 3, 2 |
Multiply the prime numbers at the bottom and the left side.
2 x 3 x 5 x 7 x 163 x 3 x 2 = 205380
Therefore, the lowest common multiple of 489,630,420 is 205380.
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.
489 x 630 x 420 = 129389400
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.
489 : 1, 3, 163, 489
630 : 1, 2, 3, 5, 6, 7, 9, 10, 14, 15, 18, 21, 30, 35, 42, 45, 63, 70, 90, 105, 126, 210, 315, 630
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
3 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 489,630,420, is 3.
Now, the common factors can be found like this.
489:3x 163
630:2x 3x 3x 5x 7
420:2x 2x 3x 5x 7
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 5x 7 = 210
Therefore, the value for common factors is 210.
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 = 129389400/(3x210)
LCM = 129389400/630
LCM = 205380
Thus, we can understand that the LCM of 489,630,420 is 205380.
LCM of two or more Numbers Calculation Examples
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FAQs on LCM of 489, 630, 420
1. What is the LCM of 489, 630, 420?
Answer: LCM of 489, 630, 420 is 205380.
2. How to calculate the LCM of 489, 630, 420?
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 489, 630, 420.
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}.