LCM of 230, 420, 824, 714
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 230, 420, 824, 714 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 230, 420, 824, 714. So, keep reading to learn more.
Given numbers are 230,420,824,714
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 230,420,824,714 is 33829320.
Find LCM of 230,420,824,714 with Prime Factorization
| 2 | 230, 420, 824, 714 |
| 2 | 115, 210, 412, 357 |
| 3 | 115, 105, 206, 357 |
| 5 | 115, 35, 206, 119 |
| 7 | 23, 7, 206, 119 |
| 23, 1, 206, 17 |
Multiply the prime numbers at the bottom and the left side.
2 x 2 x 3 x 5 x 7 x 23 x 1 x 206 x 17 = 33829320
Therefore, the lowest common multiple of 230,420,824,714 is 33829320.
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.
230 x 420 x 824 x 714 = 56833257600
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.
230 : 1, 2, 5, 10, 23, 46, 115, 230
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
824 : 1, 2, 4, 8, 103, 206, 412, 824
714 : 1, 2, 3, 6, 7, 14, 17, 21, 34, 42, 51, 102, 119, 238, 357, 714
2 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 230,420,824,714, is 2.
Now, the common factors can be found like this.
230:2x 5x 23
420:2x 2x 3x 5x 7
824:2x 2x 2x 103
714:2x 3x 7x 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 5x 7 = 840
Therefore, the value for common factors is 840.
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 = 56833257600/(2x840)
LCM = 56833257600/1680
LCM = 33829320
Thus, we can understand that the LCM of 230,420,824,714 is 33829320.
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FAQs on LCM of 230, 420, 824, 714
1. What is the LCM of 230, 420, 824, 714?
Answer: LCM of 230, 420, 824, 714 is 33829320.
2. How to calculate the LCM of 230, 420, 824, 714?
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 230, 420, 824, 714.
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}.