LCM of 829, 399, 140, 135, 420
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 829, 399, 140, 135, 420 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 829, 399, 140, 135, 420. So, keep reading to learn more.
Given numbers are 829,399,140,135,420
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 829,399,140,135,420 is 59538780.
Find LCM of 829,399,140,135,420 with Prime Factorization
| 2 | 829, 399, 140, 135, 420 |
| 2 | 829, 399, 70, 135, 210 |
| 3 | 829, 399, 35, 135, 105 |
| 5 | 829, 133, 35, 45, 35 |
| 7 | 829, 133, 7, 9, 7 |
| 829, 19, 1, 9, 1 |
Multiply the prime numbers at the bottom and the left side.
2 x 2 x 3 x 5 x 7 x 829 x 19 x 1 x 9 x 1 = 59538780
Therefore, the lowest common multiple of 829,399,140,135,420 is 59538780.
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.
829 x 399 x 140 x 135 x 420 = 2625660198000
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.
829 : 1, 829
399 : 1, 3, 7, 19, 21, 57, 133, 399
140 : 1, 2, 4, 5, 7, 10, 14, 20, 28, 35, 70, 140
135 : 1, 3, 5, 9, 15, 27, 45, 135
420 : 1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 28, 30, 35, 42, 60, 70, 84, 105, 140, 210, 420
1 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 829,399,140,135,420, is 1.
Now, the common factors can be found like this.
829:829
399:3x 7x 19
140:2x 2x 5x 7
135:3x 3x 3x 5
420:2x 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 3x 3x 5x 5x 7x 7 = 44100
Therefore, the value for common factors is 44100.
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 = 2625660198000/(1x44100)
LCM = 2625660198000/44100
LCM = 59538780
Thus, we can understand that the LCM of 829,399,140,135,420 is 59538780.
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FAQs on LCM of 829, 399, 140, 135, 420
1. What is the LCM of 829, 399, 140, 135, 420?
Answer: LCM of 829, 399, 140, 135, 420 is 59538780.
2. How to calculate the LCM of 829, 399, 140, 135, 420?
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 829, 399, 140, 135, 420.
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}.