LCM of 267, 354, 312, 300
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 267, 354, 312, 300 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 267, 354, 312, 300. So, keep reading to learn more.
Given numbers are 267,354,312,300
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 267,354,312,300 is 40957800.
Find LCM of 267,354,312,300 with Prime Factorization
| 2 | 267, 354, 312, 300 |
| 2 | 267, 177, 156, 150 |
| 3 | 267, 177, 78, 75 |
| 89, 59, 26, 25 |
Multiply the prime numbers at the bottom and the left side.
2 x 2 x 3 x 89 x 59 x 26 x 25 = 40957800
Therefore, the lowest common multiple of 267,354,312,300 is 40957800.
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.
267 x 354 x 312 x 300 = 8846884800
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.
267 : 1, 3, 89, 267
354 : 1, 2, 3, 6, 59, 118, 177, 354
312 : 1, 2, 3, 4, 6, 8, 12, 13, 24, 26, 39, 52, 78, 104, 156, 312
300 : 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 60, 75, 100, 150, 300
3 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 267,354,312,300, is 3.
Now, the common factors can be found like this.
267:3x 89
354:2x 3x 59
312:2x 2x 2x 3x 13
300:2x 2x 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 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 = 8846884800/(3x72)
LCM = 8846884800/216
LCM = 40957800
Thus, we can understand that the LCM of 267,354,312,300 is 40957800.
LCM of two or more Numbers Calculation Examples
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FAQs on LCM of 267, 354, 312, 300
1. What is the LCM of 267, 354, 312, 300?
Answer: LCM of 267, 354, 312, 300 is 40957800.
2. How to calculate the LCM of 267, 354, 312, 300?
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 267, 354, 312, 300.
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}.