LCM of 768, 342, 312, 209, 264
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 768, 342, 312, 209, 264 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 768, 342, 312, 209, 264. So, keep reading to learn more.
Given numbers are 768,342,312,209,264
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 768,342,312,209,264 is 6259968.
Find LCM of 768,342,312,209,264 with Prime Factorization
| 2 | 768, 342, 312, 209, 264 |
| 2 | 384, 171, 156, 209, 132 |
| 2 | 192, 171, 78, 209, 66 |
| 3 | 96, 171, 39, 209, 33 |
| 11 | 32, 57, 13, 209, 11 |
| 19 | 32, 57, 13, 19, 1 |
| 32, 3, 13, 1, 1 |
Multiply the prime numbers at the bottom and the left side.
2 x 2 x 2 x 3 x 11 x 19 x 32 x 3 x 13 x 1 x 1 = 6259968
Therefore, the lowest common multiple of 768,342,312,209,264 is 6259968.
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.
768 x 342 x 312 x 209 x 264 = 4521599926272
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.
768 : 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 128, 192, 256, 384, 768
342 : 1, 2, 3, 6, 9, 18, 19, 38, 57, 114, 171, 342
312 : 1, 2, 3, 4, 6, 8, 12, 13, 24, 26, 39, 52, 78, 104, 156, 312
209 : 1, 11, 19, 209
264 : 1, 2, 3, 4, 6, 8, 11, 12, 22, 24, 33, 44, 66, 88, 132, 264
1 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 768,342,312,209,264, is 1.
Now, the common factors can be found like this.
768:2x 2x 2x 2x 2x 2x 2x 2x 3
342:2x 3x 3x 19
312:2x 2x 2x 3x 13
209:11x 19
264:2x 2x 2x 3x 11
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 2x 3x 3x 3x 11x 19 = 722304
Therefore, the value for common factors is 722304.
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 = 4521599926272/(1x722304)
LCM = 4521599926272/722304
LCM = 6259968
Thus, we can understand that the LCM of 768,342,312,209,264 is 6259968.
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FAQs on LCM of 768, 342, 312, 209, 264
1. What is the LCM of 768, 342, 312, 209, 264?
Answer: LCM of 768, 342, 312, 209, 264 is 6259968.
2. How to calculate the LCM of 768, 342, 312, 209, 264?
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 768, 342, 312, 209, 264.
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}.