Find the LCM of 420, 978, 402, 684 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 420, 978, 402, 684. So, keep reading to learn more.
Given numbers are 420,978,402,684
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 420,978,402,684 is 261448740.
Find LCM of 420,978,402,684 with Prime Factorization
2 | 420, 978, 402, 684 |
2 | 210, 489, 201, 342 |
3 | 105, 489, 201, 171 |
35, 163, 67, 57 |
Multiply the prime numbers at the bottom and the left side.
2 x 2 x 3 x 35 x 163 x 67 x 57 = 261448740
Therefore, the lowest common multiple of 420,978,402,684 is 261448740.
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.
420 x 978 x 402 x 684 = 112945855680
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.
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
978 : 1, 2, 3, 6, 163, 326, 489, 978
402 : 1, 2, 3, 6, 67, 134, 201, 402
684 : 1, 2, 3, 4, 6, 9, 12, 18, 19, 36, 38, 57, 76, 114, 171, 228, 342, 684
6 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 420,978,402,684, is 6.
Now, the common factors can be found like this.
420:2x 2x 3x 5x 7
978:2x 3x 163
402:2x 3x 67
684:2x 2x 3x 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 3x 3 = 72
Therefore, the value for common factors is 72.
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 = 112945855680/(6x72)
LCM = 112945855680/432
LCM = 261448740
Thus, we can understand that the LCM of 420,978,402,684 is 261448740.
Here are some samples of LCM of two or more Numbers calculations.
1. What is the LCM of 420, 978, 402, 684?
Answer: LCM of 420, 978, 402, 684 is 261448740.
2. How to calculate the LCM of 420, 978, 402, 684?
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 420, 978, 402, 684.
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}.