LCM of 408, 749, 840, 975
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 408, 749, 840, 975 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 408, 749, 840, 975. So, keep reading to learn more.
Given numbers are 408,749,840,975
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 408,749,840,975 is 99317400.
Find LCM of 408,749,840,975 with Prime Factorization
| 2 | 408, 749, 840, 975 |
| 2 | 204, 749, 420, 975 |
| 2 | 102, 749, 210, 975 |
| 3 | 51, 749, 105, 975 |
| 5 | 17, 749, 35, 325 |
| 7 | 17, 749, 7, 65 |
| 17, 107, 1, 65 |
Multiply the prime numbers at the bottom and the left side.
2 x 2 x 2 x 3 x 5 x 7 x 17 x 107 x 1 x 65 = 99317400
Therefore, the lowest common multiple of 408,749,840,975 is 99317400.
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.
408 x 749 x 840 x 975 = 250279848000
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.
408 : 1, 2, 3, 4, 6, 8, 12, 17, 24, 34, 51, 68, 102, 136, 204, 408
749 : 1, 7, 107, 749
840 : 1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 20, 21, 24, 28, 30, 35, 40, 42, 56, 60, 70, 84, 105, 120, 140, 168, 210, 280, 420, 840
975 : 1, 3, 5, 13, 15, 25, 39, 65, 75, 195, 325, 975
1 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 408,749,840,975, is 1.
Now, the common factors can be found like this.
408:2x 2x 2x 3x 17
749:7x 107
840:2x 2x 2x 3x 5x 7
975:3x 5x 5x 13
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 3x 5x 7 = 2520
Therefore, the value for common factors is 2520.
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 = 250279848000/(1x2520)
LCM = 250279848000/2520
LCM = 99317400
Thus, we can understand that the LCM of 408,749,840,975 is 99317400.
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FAQs on LCM of 408, 749, 840, 975
1. What is the LCM of 408, 749, 840, 975?
Answer: LCM of 408, 749, 840, 975 is 99317400.
2. How to calculate the LCM of 408, 749, 840, 975?
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 408, 749, 840, 975.
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}.