LCM of 384, 540, 351, 690
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 384, 540, 351, 690 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 384, 540, 351, 690. So, keep reading to learn more.
Given numbers are 384,540,351,690
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 384,540,351,690 is 5166720.
Find LCM of 384,540,351,690 with Prime Factorization
| 2 | 384, 540, 351, 690 |
| 2 | 192, 270, 351, 345 |
| 3 | 96, 135, 351, 345 |
| 3 | 32, 45, 117, 115 |
| 3 | 32, 15, 39, 115 |
| 5 | 32, 5, 13, 115 |
| 32, 1, 13, 23 |
Multiply the prime numbers at the bottom and the left side.
2 x 2 x 3 x 3 x 3 x 5 x 32 x 1 x 13 x 23 = 5166720
Therefore, the lowest common multiple of 384,540,351,690 is 5166720.
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.
384 x 540 x 351 x 690 = 50220518400
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.
384 : 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 128, 192, 384
540 : 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 27, 30, 36, 45, 54, 60, 90, 108, 135, 180, 270, 540
351 : 1, 3, 9, 13, 27, 39, 117, 351
690 : 1, 2, 3, 5, 6, 10, 15, 23, 30, 46, 69, 115, 138, 230, 345, 690
3 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 384,540,351,690, is 3.
Now, the common factors can be found like this.
384:2x 2x 2x 2x 2x 2x 2x 3
540:2x 2x 3x 3x 3x 5
351:3x 3x 3x 13
690:2x 3x 5x 23
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 3x 5 = 3240
Therefore, the value for common factors is 3240.
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 = 50220518400/(3x3240)
LCM = 50220518400/9720
LCM = 5166720
Thus, we can understand that the LCM of 384,540,351,690 is 5166720.
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FAQs on LCM of 384, 540, 351, 690
1. What is the LCM of 384, 540, 351, 690?
Answer: LCM of 384, 540, 351, 690 is 5166720.
2. How to calculate the LCM of 384, 540, 351, 690?
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 384, 540, 351, 690.
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}.