LCM of 489, 624, 120, 962, 900
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 489, 624, 120, 962, 900 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, 624, 120, 962, 900. So, keep reading to learn more.
Given numbers are 489,624,120,962,900
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 489,624,120,962,900 is 282250800.
Find LCM of 489,624,120,962,900 with Prime Factorization
| 2 | 489, 624, 120, 962, 900 |
| 2 | 489, 312, 60, 481, 450 |
| 2 | 489, 156, 30, 481, 225 |
| 3 | 489, 78, 15, 481, 225 |
| 5 | 163, 26, 5, 481, 75 |
| 13 | 163, 26, 1, 481, 15 |
| 163, 2, 1, 37, 15 |
Multiply the prime numbers at the bottom and the left side.
2 x 2 x 2 x 3 x 5 x 13 x 163 x 2 x 1 x 37 x 15 = 282250800
Therefore, the lowest common multiple of 489,624,120,962,900 is 282250800.
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 624 x 120 x 962 x 900 = 31702409856000
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
624 : 1, 2, 3, 4, 6, 8, 12, 13, 16, 24, 26, 39, 48, 52, 78, 104, 156, 208, 312, 624
120 : 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120
962 : 1, 2, 13, 26, 37, 74, 481, 962
900 : 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 25, 30, 36, 45, 50, 60, 75, 90, 100, 150, 180, 225, 300, 450, 900
1 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 489,624,120,962,900, is 1.
Now, the common factors can be found like this.
489:3x 163
624:2x 2x 2x 2x 3x 13
120:2x 2x 2x 3x 5
962:2x 13x 37
900:2x 2x 3x 3x 5x 5
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 2x 2x 3x 3x 3x 5x 13 = 112320
Therefore, the value for common factors is 112320.
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 = 31702409856000/(1x112320)
LCM = 31702409856000/112320
LCM = 282250800
Thus, we can understand that the LCM of 489,624,120,962,900 is 282250800.
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FAQs on LCM of 489, 624, 120, 962, 900
1. What is the LCM of 489, 624, 120, 962, 900?
Answer: LCM of 489, 624, 120, 962, 900 is 282250800.
2. How to calculate the LCM of 489, 624, 120, 962, 900?
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, 624, 120, 962, 900.
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}.