LCM of 189, 756, 210, 578
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 189, 756, 210, 578 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 189, 756, 210, 578. So, keep reading to learn more.
Given numbers are 189,756,210,578
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 189,756,210,578 is 1092420.
Find LCM of 189,756,210,578 with Prime Factorization
| 2 | 189, 756, 210, 578 |
| 3 | 189, 378, 105, 289 |
| 3 | 63, 126, 35, 289 |
| 3 | 21, 42, 35, 289 |
| 7 | 7, 14, 35, 289 |
| 1, 2, 5, 289 |
Multiply the prime numbers at the bottom and the left side.
2 x 3 x 3 x 3 x 7 x 1 x 2 x 5 x 289 = 1092420
Therefore, the lowest common multiple of 189,756,210,578 is 1092420.
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.
189 x 756 x 210 x 578 = 17343259920
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.
189 : 1, 3, 7, 9, 21, 27, 63, 189
756 : 1, 2, 3, 4, 6, 7, 9, 12, 14, 18, 21, 27, 28, 36, 42, 54, 63, 84, 108, 126, 189, 252, 378, 756
210 : 1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 30, 35, 42, 70, 105, 210
578 : 1, 2, 17, 34, 289, 578
1 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 189,756,210,578, is 1.
Now, the common factors can be found like this.
189:3x 3x 3x 7
756:2x 2x 3x 3x 3x 7
210:2x 3x 5x 7
578:2x 17x 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 3x 3x 3x 3x 7x 7 = 15876
Therefore, the value for common factors is 15876.
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 = 17343259920/(1x15876)
LCM = 17343259920/15876
LCM = 1092420
Thus, we can understand that the LCM of 189,756,210,578 is 1092420.
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FAQs on LCM of 189, 756, 210, 578
1. What is the LCM of 189, 756, 210, 578?
Answer: LCM of 189, 756, 210, 578 is 1092420.
2. How to calculate the LCM of 189, 756, 210, 578?
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 189, 756, 210, 578.
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}.