LCM of 219, 360, 123, 397, 840
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 219, 360, 123, 397, 840 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 219, 360, 123, 397, 840. So, keep reading to learn more.
Given numbers are 219,360,123,397,840
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 219,360,123,397,840 is 2994316920.
Find LCM of 219,360,123,397,840 with Prime Factorization
| 2 | 219, 360, 123, 397, 840 |
| 2 | 219, 180, 123, 397, 420 |
| 2 | 219, 90, 123, 397, 210 |
| 3 | 219, 45, 123, 397, 105 |
| 5 | 73, 15, 41, 397, 35 |
| 73, 3, 41, 397, 7 |
Multiply the prime numbers at the bottom and the left side.
2 x 2 x 2 x 3 x 5 x 73 x 3 x 41 x 397 x 7 = 2994316920
Therefore, the lowest common multiple of 219,360,123,397,840 is 2994316920.
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.
219 x 360 x 123 x 397 x 840 = 3233862273600
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.
219 : 1, 3, 73, 219
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
123 : 1, 3, 41, 123
397 : 1, 397
840 : 1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 20, 21, 24, 28, 30, 35, 40, 42, 56, 60, 70, 84, 105, 120, 140, 168, 210, 280, 420, 840
1 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 219,360,123,397,840, is 1.
Now, the common factors can be found like this.
219:3x 73
360:2x 2x 2x 3x 3x 5
123:3x 41
397:397
840:2x 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 2x 2x 3x 3x 3x 5 = 1080
Therefore, the value for common factors is 1080.
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 = 3233862273600/(1x1080)
LCM = 3233862273600/1080
LCM = 2994316920
Thus, we can understand that the LCM of 219,360,123,397,840 is 2994316920.
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FAQs on LCM of 219, 360, 123, 397, 840
1. What is the LCM of 219, 360, 123, 397, 840?
Answer: LCM of 219, 360, 123, 397, 840 is 2994316920.
2. How to calculate the LCM of 219, 360, 123, 397, 840?
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 219, 360, 123, 397, 840.
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}.