LCM of 338, 522, 240, 420, 420
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 338, 522, 240, 420, 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 338, 522, 240, 420, 420. So, keep reading to learn more.
Given numbers are 338,522,240,420,420
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 338,522,240,420,420 is 24701040.
Find LCM of 338,522,240,420,420 with Prime Factorization
| 2 | 338, 522, 240, 420, 420 |
| 2 | 169, 261, 120, 210, 210 |
| 3 | 169, 261, 60, 105, 105 |
| 5 | 169, 87, 20, 35, 35 |
| 7 | 169, 87, 4, 7, 7 |
| 169, 87, 4, 1, 1 |
Multiply the prime numbers at the bottom and the left side.
2 x 2 x 3 x 5 x 7 x 169 x 87 x 4 x 1 x 1 = 24701040
Therefore, the lowest common multiple of 338,522,240,420,420 is 24701040.
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.
338 x 522 x 240 x 420 x 420 = 7469594496000
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.
338 : 1, 2, 13, 26, 169, 338
522 : 1, 2, 3, 6, 9, 18, 29, 58, 87, 174, 261, 522
240 : 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 40, 48, 60, 80, 120, 240
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
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
2 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 338,522,240,420,420, is 2.
Now, the common factors can be found like this.
338:2x 13x 13
522:2x 3x 3x 29
240:2x 2x 2x 2x 3x 5
420:2x 2x 3x 5x 7
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 2x 2x 2x 3x 3x 3x 5x 5x 7 = 151200
Therefore, the value for common factors is 151200.
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 = 7469594496000/(2x151200)
LCM = 7469594496000/302400
LCM = 24701040
Thus, we can understand that the LCM of 338,522,240,420,420 is 24701040.
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FAQs on LCM of 338, 522, 240, 420, 420
1. What is the LCM of 338, 522, 240, 420, 420?
Answer: LCM of 338, 522, 240, 420, 420 is 24701040.
2. How to calculate the LCM of 338, 522, 240, 420, 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 338, 522, 240, 420, 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}.