LCM of 168, 728, 462, 312, 450
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 168, 728, 462, 312, 450 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 168, 728, 462, 312, 450. So, keep reading to learn more.
Given numbers are 168,728,462,312,450
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 168,728,462,312,450 is 1801800.
Find LCM of 168,728,462,312,450 with Prime Factorization
| 2 | 168, 728, 462, 312, 450 |
| 2 | 84, 364, 231, 156, 225 |
| 2 | 42, 182, 231, 78, 225 |
| 3 | 21, 91, 231, 39, 225 |
| 7 | 7, 91, 77, 13, 75 |
| 13 | 1, 13, 11, 13, 75 |
| 1, 1, 11, 1, 75 |
Multiply the prime numbers at the bottom and the left side.
2 x 2 x 2 x 3 x 7 x 13 x 1 x 1 x 11 x 1 x 75 = 1801800
Therefore, the lowest common multiple of 168,728,462,312,450 is 1801800.
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.
168 x 728 x 462 x 312 x 450 = 7933224499200
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.
168 : 1, 2, 3, 4, 6, 7, 8, 12, 14, 21, 24, 28, 42, 56, 84, 168
728 : 1, 2, 4, 7, 8, 13, 14, 26, 28, 52, 56, 91, 104, 182, 364, 728
462 : 1, 2, 3, 6, 7, 11, 14, 21, 22, 33, 42, 66, 77, 154, 231, 462
312 : 1, 2, 3, 4, 6, 8, 12, 13, 24, 26, 39, 52, 78, 104, 156, 312
450 : 1, 2, 3, 5, 6, 9, 10, 15, 18, 25, 30, 45, 50, 75, 90, 150, 225, 450
2 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 168,728,462,312,450, is 2.
Now, the common factors can be found like this.
168:2x 2x 2x 3x 7
728:2x 2x 2x 7x 13
462:2x 3x 7x 11
312:2x 2x 2x 3x 13
450:2x 3x 3x 5x 5
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 3x 7x 7x 13 = 2201472
Therefore, the value for common factors is 2201472.
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 = 7933224499200/(2x2201472)
LCM = 7933224499200/4402944
LCM = 1801800
Thus, we can understand that the LCM of 168,728,462,312,450 is 1801800.
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FAQs on LCM of 168, 728, 462, 312, 450
1. What is the LCM of 168, 728, 462, 312, 450?
Answer: LCM of 168, 728, 462, 312, 450 is 1801800.
2. How to calculate the LCM of 168, 728, 462, 312, 450?
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 168, 728, 462, 312, 450.
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}.