LCM of 457, 420, 460, 375
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 457, 420, 460, 375 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 457, 420, 460, 375. So, keep reading to learn more.
Given numbers are 457,420,460,375
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 457,420,460,375 is 110365500.
Find LCM of 457,420,460,375 with Prime Factorization
| 2 | 457, 420, 460, 375 |
| 2 | 457, 210, 230, 375 |
| 3 | 457, 105, 115, 375 |
| 5 | 457, 35, 115, 125 |
| 457, 7, 23, 25 |
Multiply the prime numbers at the bottom and the left side.
2 x 2 x 3 x 5 x 457 x 7 x 23 x 25 = 110365500
Therefore, the lowest common multiple of 457,420,460,375 is 110365500.
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.
457 x 420 x 460 x 375 = 33109650000
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.
457 : 1, 457
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
460 : 1, 2, 4, 5, 10, 20, 23, 46, 92, 115, 230, 460
375 : 1, 3, 5, 15, 25, 75, 125, 375
1 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 457,420,460,375, is 1.
Now, the common factors can be found like this.
457:457
420:2x 2x 3x 5x 7
460:2x 2x 5x 23
375:3x 5x 5x 5
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 5x 5 = 300
Therefore, the value for common factors is 300.
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 = 33109650000/(1x300)
LCM = 33109650000/300
LCM = 110365500
Thus, we can understand that the LCM of 457,420,460,375 is 110365500.
LCM of two or more Numbers Calculation Examples
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FAQs on LCM of 457, 420, 460, 375
1. What is the LCM of 457, 420, 460, 375?
Answer: LCM of 457, 420, 460, 375 is 110365500.
2. How to calculate the LCM of 457, 420, 460, 375?
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 457, 420, 460, 375.
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}.