LCM of 714, 540, 321, 300, 378
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 714, 540, 321, 300, 378 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 714, 540, 321, 300, 378. So, keep reading to learn more.
Given numbers are 714,540,321,300,378
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 714,540,321,300,378 is 34379100.
Find LCM of 714,540,321,300,378 with Prime Factorization
| 2 | 714, 540, 321, 300, 378 |
| 2 | 357, 270, 321, 150, 189 |
| 3 | 357, 135, 321, 75, 189 |
| 3 | 119, 45, 107, 25, 63 |
| 3 | 119, 15, 107, 25, 21 |
| 5 | 119, 5, 107, 25, 7 |
| 7 | 119, 1, 107, 5, 7 |
| 17, 1, 107, 5, 1 |
Multiply the prime numbers at the bottom and the left side.
2 x 2 x 3 x 3 x 3 x 5 x 7 x 17 x 1 x 107 x 5 x 1 = 34379100
Therefore, the lowest common multiple of 714,540,321,300,378 is 34379100.
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.
714 x 540 x 321 x 300 x 378 = 14034923784000
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.
714 : 1, 2, 3, 6, 7, 14, 17, 21, 34, 42, 51, 102, 119, 238, 357, 714
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
321 : 1, 3, 107, 321
300 : 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 60, 75, 100, 150, 300
378 : 1, 2, 3, 6, 7, 9, 14, 18, 21, 27, 42, 54, 63, 126, 189, 378
3 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 714,540,321,300,378, is 3.
Now, the common factors can be found like this.
714:2x 3x 7x 17
540:2x 2x 3x 3x 3x 5
321:3x 107
300:2x 2x 3x 5x 5
378:2x 3x 3x 3x 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 3x 3x 3x 3x 5x 7 = 136080
Therefore, the value for common factors is 136080.
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 = 14034923784000/(3x136080)
LCM = 14034923784000/408240
LCM = 34379100
Thus, we can understand that the LCM of 714,540,321,300,378 is 34379100.
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FAQs on LCM of 714, 540, 321, 300, 378
1. What is the LCM of 714, 540, 321, 300, 378?
Answer: LCM of 714, 540, 321, 300, 378 is 34379100.
2. How to calculate the LCM of 714, 540, 321, 300, 378?
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 714, 540, 321, 300, 378.
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}.