LCM of 219, 342, 264, 840
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 219, 342, 264, 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, 342, 264, 840. So, keep reading to learn more.
Given numbers are 219,342,264,840
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 219,342,264,840 is 38447640.
Find LCM of 219,342,264,840 with Prime Factorization
| 2 | 219, 342, 264, 840 |
| 2 | 219, 171, 132, 420 |
| 2 | 219, 171, 66, 210 |
| 3 | 219, 171, 33, 105 |
| 73, 57, 11, 35 |
Multiply the prime numbers at the bottom and the left side.
2 x 2 x 2 x 3 x 73 x 57 x 11 x 35 = 38447640
Therefore, the lowest common multiple of 219,342,264,840 is 38447640.
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 342 x 264 x 840 = 16609380480
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
342 : 1, 2, 3, 6, 9, 18, 19, 38, 57, 114, 171, 342
264 : 1, 2, 3, 4, 6, 8, 11, 12, 22, 24, 33, 44, 66, 88, 132, 264
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
3 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 219,342,264,840, is 3.
Now, the common factors can be found like this.
219:3x 73
342:2x 3x 3x 19
264:2x 2x 2x 3x 11
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 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 = 16609380480/(3x144)
LCM = 16609380480/432
LCM = 38447640
Thus, we can understand that the LCM of 219,342,264,840 is 38447640.
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FAQs on LCM of 219, 342, 264, 840
1. What is the LCM of 219, 342, 264, 840?
Answer: LCM of 219, 342, 264, 840 is 38447640.
2. How to calculate the LCM of 219, 342, 264, 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, 342, 264, 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}.