LCM of 329, 378, 398, 420
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 329, 378, 398, 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 329, 378, 398, 420. So, keep reading to learn more.
Given numbers are 329,378,398,420
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 329,378,398,420 is 35354340.
Find LCM of 329,378,398,420 with Prime Factorization
| 2 | 329, 378, 398, 420 |
| 3 | 329, 189, 199, 210 |
| 7 | 329, 63, 199, 70 |
| 47, 9, 199, 10 |
Multiply the prime numbers at the bottom and the left side.
2 x 3 x 7 x 47 x 9 x 199 x 10 = 35354340
Therefore, the lowest common multiple of 329,378,398,420 is 35354340.
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.
329 x 378 x 398 x 420 = 20788351920
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.
329 : 1, 7, 47, 329
378 : 1, 2, 3, 6, 7, 9, 14, 18, 21, 27, 42, 54, 63, 126, 189, 378
398 : 1, 2, 199, 398
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 329,378,398,420, is 1.
Now, the common factors can be found like this.
329:7x 47
378:2x 3x 3x 3x 7
398:2x 199
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 7x 7 = 588
Therefore, the value for common factors is 588.
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 = 20788351920/(1x588)
LCM = 20788351920/588
LCM = 35354340
Thus, we can understand that the LCM of 329,378,398,420 is 35354340.
LCM of two or more Numbers Calculation Examples
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FAQs on LCM of 329, 378, 398, 420
1. What is the LCM of 329, 378, 398, 420?
Answer: LCM of 329, 378, 398, 420 is 35354340.
2. How to calculate the LCM of 329, 378, 398, 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 329, 378, 398, 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}.