LCM of 678, 971, 120, 404, 354
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 678, 971, 120, 404, 354 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 678, 971, 120, 404, 354. So, keep reading to learn more.
Given numbers are 678,971,120,404,354
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 678,971,120,404,354 is 78460722840.
Find LCM of 678,971,120,404,354 with Prime Factorization
| 2 | 678, 971, 120, 404, 354 |
| 2 | 339, 971, 60, 202, 177 |
| 3 | 339, 971, 30, 101, 177 |
| 113, 971, 10, 101, 59 |
Multiply the prime numbers at the bottom and the left side.
2 x 2 x 3 x 113 x 971 x 10 x 101 x 59 = 78460722840
Therefore, the lowest common multiple of 678,971,120,404,354 is 78460722840.
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.
678 x 971 x 120 x 404 x 354 = 11298344088960
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.
678 : 1, 2, 3, 6, 113, 226, 339, 678
971 : 1, 971
120 : 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120
404 : 1, 2, 4, 101, 202, 404
354 : 1, 2, 3, 6, 59, 118, 177, 354
1 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 678,971,120,404,354, is 1.
Now, the common factors can be found like this.
678:2x 3x 113
971:971
120:2x 2x 2x 3x 5
404:2x 2x 101
354:2x 3x 59
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 3 = 144
Therefore, the value for common factors is 144.
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 = 11298344088960/(1x144)
LCM = 11298344088960/144
LCM = 78460722840
Thus, we can understand that the LCM of 678,971,120,404,354 is 78460722840.
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FAQs on LCM of 678, 971, 120, 404, 354
1. What is the LCM of 678, 971, 120, 404, 354?
Answer: LCM of 678, 971, 120, 404, 354 is 78460722840.
2. How to calculate the LCM of 678, 971, 120, 404, 354?
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 678, 971, 120, 404, 354.
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}.