LCM of 768, 144, 172, 689
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 768, 144, 172, 689 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 768, 144, 172, 689. So, keep reading to learn more.
Given numbers are 768,144,172,689
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 768,144,172,689 is 68260608.
Find LCM of 768,144,172,689 with Prime Factorization
| 2 | 768, 144, 172, 689 |
| 2 | 384, 72, 86, 689 |
| 2 | 192, 36, 43, 689 |
| 2 | 96, 18, 43, 689 |
| 3 | 48, 9, 43, 689 |
| 16, 3, 43, 689 |
Multiply the prime numbers at the bottom and the left side.
2 x 2 x 2 x 2 x 3 x 16 x 3 x 43 x 689 = 68260608
Therefore, the lowest common multiple of 768,144,172,689 is 68260608.
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.
768 x 144 x 172 x 689 = 13106036736
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.
768 : 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 128, 192, 256, 384, 768
144 : 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144
172 : 1, 2, 4, 43, 86, 172
689 : 1, 13, 53, 689
1 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 768,144,172,689, is 1.
Now, the common factors can be found like this.
768:2x 2x 2x 2x 2x 2x 2x 2x 3
144:2x 2x 2x 2x 3x 3
172:2x 2x 43
689:13x 53
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 2x 2x 3 = 192
Therefore, the value for common factors is 192.
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 = 13106036736/(1x192)
LCM = 13106036736/192
LCM = 68260608
Thus, we can understand that the LCM of 768,144,172,689 is 68260608.
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FAQs on LCM of 768, 144, 172, 689
1. What is the LCM of 768, 144, 172, 689?
Answer: LCM of 768, 144, 172, 689 is 68260608.
2. How to calculate the LCM of 768, 144, 172, 689?
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 768, 144, 172, 689.
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}.