LCM of 546, 375, 840
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 546, 375, 840 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 546, 375, 840. So, keep reading to learn more.
Given numbers are 546,375,840
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 546,375,840 is 273000.
Find LCM of 546,375,840 with Prime Factorization
| 2 | 546, 375, 840 |
| 3 | 273, 375, 420 |
| 5 | 91, 125, 140 |
| 7 | 91, 25, 28 |
| 13, 25, 4 |
Multiply the prime numbers at the bottom and the left side.
2 x 3 x 5 x 7 x 13 x 25 x 4 = 273000
Therefore, the lowest common multiple of 546,375,840 is 273000.
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.
546 x 375 x 840 = 171990000
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.
546 : 1, 2, 3, 6, 7, 13, 14, 21, 26, 39, 42, 78, 91, 182, 273, 546
375 : 1, 3, 5, 15, 25, 75, 125, 375
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
3 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 546,375,840, is 3.
Now, the common factors can be found like this.
546:2x 3x 7x 13
375:3x 5x 5x 5
840:2x 2x 2x 3x 5x 7
From this, we can see that the common factors because they appear for more than two numbers. So, just multiply them all together.
2x 3x 5x 7 = 210
Therefore, the value for common factors is 210.
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 = 171990000/(3x210)
LCM = 171990000/630
LCM = 273000
Thus, we can understand that the LCM of 546,375,840 is 273000.
LCM of two or more Numbers Calculation Examples
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FAQs on LCM of 546, 375, 840
1. What is the LCM of 546, 375, 840?
Answer: LCM of 546, 375, 840 is 273000.
2. How to calculate the LCM of 546, 375, 840?
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 546, 375, 840.
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}.