LCM of 460, 275, 278, 420
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 460, 275, 278, 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 460, 275, 278, 420. So, keep reading to learn more.
Given numbers are 460,275,278,420
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 460,275,278,420 is 73850700.
Find LCM of 460,275,278,420 with Prime Factorization
| 2 | 460, 275, 278, 420 |
| 2 | 230, 275, 139, 210 |
| 5 | 115, 275, 139, 105 |
| 23, 55, 139, 21 |
Multiply the prime numbers at the bottom and the left side.
2 x 2 x 5 x 23 x 55 x 139 x 21 = 73850700
Therefore, the lowest common multiple of 460,275,278,420 is 73850700.
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.
460 x 275 x 278 x 420 = 14770140000
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.
460 : 1, 2, 4, 5, 10, 20, 23, 46, 92, 115, 230, 460
275 : 1, 5, 11, 25, 55, 275
278 : 1, 2, 139, 278
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 460,275,278,420, is 1.
Now, the common factors can be found like this.
460:2x 2x 5x 23
275:5x 5x 11
278:2x 139
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 5x 5 = 200
Therefore, the value for common factors is 200.
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 = 14770140000/(1x200)
LCM = 14770140000/200
LCM = 73850700
Thus, we can understand that the LCM of 460,275,278,420 is 73850700.
LCM of two or more Numbers Calculation Examples
Here are some samples of LCM of two or more Numbers calculations.
FAQs on LCM of 460, 275, 278, 420
1. What is the LCM of 460, 275, 278, 420?
Answer: LCM of 460, 275, 278, 420 is 73850700.
2. How to calculate the LCM of 460, 275, 278, 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 460, 275, 278, 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}.