LCM of 123, 178, 312, 608, 456
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 123, 178, 312, 608, 456 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 123, 178, 312, 608, 456. So, keep reading to learn more.
Given numbers are 123,178,312,608,456
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 123,178,312,608,456 is 86525088.
Find LCM of 123,178,312,608,456 with Prime Factorization
| 2 | 123, 178, 312, 608, 456 |
| 2 | 123, 89, 156, 304, 228 |
| 2 | 123, 89, 78, 152, 114 |
| 3 | 123, 89, 39, 76, 57 |
| 19 | 41, 89, 13, 76, 19 |
| 41, 89, 13, 4, 1 |
Multiply the prime numbers at the bottom and the left side.
2 x 2 x 2 x 3 x 19 x 41 x 89 x 13 x 4 x 1 = 86525088
Therefore, the lowest common multiple of 123,178,312,608,456 is 86525088.
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.
123 x 178 x 312 x 608 x 456 = 1893861126144
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.
123 : 1, 3, 41, 123
178 : 1, 2, 89, 178
312 : 1, 2, 3, 4, 6, 8, 12, 13, 24, 26, 39, 52, 78, 104, 156, 312
608 : 1, 2, 4, 8, 16, 19, 32, 38, 76, 152, 304, 608
456 : 1, 2, 3, 4, 6, 8, 12, 19, 24, 38, 57, 76, 114, 152, 228, 456
1 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 123,178,312,608,456, is 1.
Now, the common factors can be found like this.
123:3x 41
178:2x 89
312:2x 2x 2x 3x 13
608:2x 2x 2x 2x 2x 19
456:2x 2x 2x 3x 19
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 2x 3x 3x 19 = 21888
Therefore, the value for common factors is 21888.
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 = 1893861126144/(1x21888)
LCM = 1893861126144/21888
LCM = 86525088
Thus, we can understand that the LCM of 123,178,312,608,456 is 86525088.
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FAQs on LCM of 123, 178, 312, 608, 456
1. What is the LCM of 123, 178, 312, 608, 456?
Answer: LCM of 123, 178, 312, 608, 456 is 86525088.
2. How to calculate the LCM of 123, 178, 312, 608, 456?
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 123, 178, 312, 608, 456.
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}.