LCM of 347, 663, 420, 450, 678
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 347, 663, 420, 450, 678 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 347, 663, 420, 450, 678. So, keep reading to learn more.
Given numbers are 347,663,420,450,678
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 347,663,420,450,678 is 54593475300.
Find LCM of 347,663,420,450,678 with Prime Factorization
| 2 | 347, 663, 420, 450, 678 |
| 3 | 347, 663, 210, 225, 339 |
| 5 | 347, 221, 70, 75, 113 |
| 347, 221, 14, 15, 113 |
Multiply the prime numbers at the bottom and the left side.
2 x 3 x 5 x 347 x 221 x 14 x 15 x 113 = 54593475300
Therefore, the lowest common multiple of 347,663,420,450,678 is 54593475300.
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.
347 x 663 x 420 x 450 x 678 = 29480476662000
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.
347 : 1, 347
663 : 1, 3, 13, 17, 39, 51, 221, 663
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
450 : 1, 2, 3, 5, 6, 9, 10, 15, 18, 25, 30, 45, 50, 75, 90, 150, 225, 450
678 : 1, 2, 3, 6, 113, 226, 339, 678
1 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 347,663,420,450,678, is 1.
Now, the common factors can be found like this.
347:347
663:3x 13x 17
420:2x 2x 3x 5x 7
450:2x 3x 3x 5x 5
678:2x 3x 113
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 5 = 540
Therefore, the value for common factors is 540.
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 = 29480476662000/(1x540)
LCM = 29480476662000/540
LCM = 54593475300
Thus, we can understand that the LCM of 347,663,420,450,678 is 54593475300.
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FAQs on LCM of 347, 663, 420, 450, 678
1. What is the LCM of 347, 663, 420, 450, 678?
Answer: LCM of 347, 663, 420, 450, 678 is 54593475300.
2. How to calculate the LCM of 347, 663, 420, 450, 678?
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 347, 663, 420, 450, 678.
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}.