LCM of 210, 409, 322, 720, 428
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 210, 409, 322, 720, 428 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 210, 409, 322, 720, 428. So, keep reading to learn more.
Given numbers are 210,409,322,720,428
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 210,409,322,720,428 is 5073006960.
Find LCM of 210,409,322,720,428 with Prime Factorization
| 2 | 210, 409, 322, 720, 428 |
| 2 | 105, 409, 161, 360, 214 |
| 3 | 105, 409, 161, 180, 107 |
| 5 | 35, 409, 161, 60, 107 |
| 7 | 7, 409, 161, 12, 107 |
| 1, 409, 23, 12, 107 |
Multiply the prime numbers at the bottom and the left side.
2 x 2 x 3 x 5 x 7 x 1 x 409 x 23 x 12 x 107 = 5073006960
Therefore, the lowest common multiple of 210,409,322,720,428 is 5073006960.
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.
210 x 409 x 322 x 720 x 428 = 8522651692800
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.
210 : 1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 30, 35, 42, 70, 105, 210
409 : 1, 409
322 : 1, 2, 7, 14, 23, 46, 161, 322
720 : 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 30, 36, 40, 45, 48, 60, 72, 80, 90, 120, 144, 180, 240, 360, 720
428 : 1, 2, 4, 107, 214, 428
1 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 210,409,322,720,428, is 1.
Now, the common factors can be found like this.
210:2x 3x 5x 7
409:409
322:2x 7x 23
720:2x 2x 2x 2x 3x 3x 5
428:2x 2x 107
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 3x 5x 7 = 1680
Therefore, the value for common factors is 1680.
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 = 8522651692800/(1x1680)
LCM = 8522651692800/1680
LCM = 5073006960
Thus, we can understand that the LCM of 210,409,322,720,428 is 5073006960.
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FAQs on LCM of 210, 409, 322, 720, 428
1. What is the LCM of 210, 409, 322, 720, 428?
Answer: LCM of 210, 409, 322, 720, 428 is 5073006960.
2. How to calculate the LCM of 210, 409, 322, 720, 428?
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 210, 409, 322, 720, 428.
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}.