LCM of 338, 209, 578, 612, 312
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 338, 209, 578, 612, 312 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 338, 209, 578, 612, 312. So, keep reading to learn more.
Given numbers are 338,209,578,612,312
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 338,209,578,612,312 is 734959368.
Find LCM of 338,209,578,612,312 with Prime Factorization
| 2 | 338, 209, 578, 612, 312 |
| 2 | 169, 209, 289, 306, 156 |
| 3 | 169, 209, 289, 153, 78 |
| 13 | 169, 209, 289, 51, 26 |
| 17 | 13, 209, 289, 51, 2 |
| 13, 209, 17, 3, 2 |
Multiply the prime numbers at the bottom and the left side.
2 x 2 x 3 x 13 x 17 x 13 x 209 x 17 x 3 x 2 = 734959368
Therefore, the lowest common multiple of 338,209,578,612,312 is 734959368.
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.
338 x 209 x 578 x 612 x 312 = 7796448975744
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.
338 : 1, 2, 13, 26, 169, 338
209 : 1, 11, 19, 209
578 : 1, 2, 17, 34, 289, 578
612 : 1, 2, 3, 4, 6, 9, 12, 17, 18, 34, 36, 51, 68, 102, 153, 204, 306, 612
312 : 1, 2, 3, 4, 6, 8, 12, 13, 24, 26, 39, 52, 78, 104, 156, 312
1 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 338,209,578,612,312, is 1.
Now, the common factors can be found like this.
338:2x 13x 13
209:11x 19
578:2x 17x 17
612:2x 2x 3x 3x 17
312:2x 2x 2x 3x 13
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 13x 17 = 10608
Therefore, the value for common factors is 10608.
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 = 7796448975744/(1x10608)
LCM = 7796448975744/10608
LCM = 734959368
Thus, we can understand that the LCM of 338,209,578,612,312 is 734959368.
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FAQs on LCM of 338, 209, 578, 612, 312
1. What is the LCM of 338, 209, 578, 612, 312?
Answer: LCM of 338, 209, 578, 612, 312 is 734959368.
2. How to calculate the LCM of 338, 209, 578, 612, 312?
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 338, 209, 578, 612, 312.
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}.