LCM of 420, 414, 216, 374
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 420, 414, 216, 374 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 420, 414, 216, 374. So, keep reading to learn more.
Given numbers are 420,414,216,374
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 420,414,216,374 is 32515560.
Find LCM of 420,414,216,374 with Prime Factorization
| 2 | 420, 414, 216, 374 |
| 2 | 210, 207, 108, 187 |
| 3 | 105, 207, 54, 187 |
| 3 | 35, 69, 18, 187 |
| 35, 23, 6, 187 |
Multiply the prime numbers at the bottom and the left side.
2 x 2 x 3 x 3 x 35 x 23 x 6 x 187 = 32515560
Therefore, the lowest common multiple of 420,414,216,374 is 32515560.
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.
420 x 414 x 216 x 374 = 14046721920
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.
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
414 : 1, 2, 3, 6, 9, 18, 23, 46, 69, 138, 207, 414
216 : 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 108, 216
374 : 1, 2, 11, 17, 22, 34, 187, 374
2 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 420,414,216,374, is 2.
Now, the common factors can be found like this.
420:2x 2x 3x 5x 7
414:2x 3x 3x 23
216:2x 2x 2x 3x 3x 3
374:2x 11x 17
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 3 = 216
Therefore, the value for common factors is 216.
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 = 14046721920/(2x216)
LCM = 14046721920/432
LCM = 32515560
Thus, we can understand that the LCM of 420,414,216,374 is 32515560.
LCM of two or more Numbers Calculation Examples
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FAQs on LCM of 420, 414, 216, 374
1. What is the LCM of 420, 414, 216, 374?
Answer: LCM of 420, 414, 216, 374 is 32515560.
2. How to calculate the LCM of 420, 414, 216, 374?
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 420, 414, 216, 374.
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}.