LCM of 252, 378, 504, 360
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 252, 378, 504, 360 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 252, 378, 504, 360. So, keep reading to learn more.
Given numbers are 252,378,504,360
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 252,378,504,360 is 7560.
Find LCM of 252,378,504,360 with Prime Factorization
| 2 | 252, 378, 504, 360 |
| 2 | 126, 189, 252, 180 |
| 2 | 63, 189, 126, 90 |
| 3 | 63, 189, 63, 45 |
| 3 | 21, 21, 63, 15 |
| 7 | 7, 7, 21, 5 |
| 1, 1, 3, 5 |
Multiply the prime numbers at the bottom and the left side.
2 x 2 x 2 x 3 x 3 x 7 x 1 x 1 x 3 x 5 = 7560
Therefore, the lowest common multiple of 252,378,504,360 is 7560.
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.
252 x 378 x 504 x 360 = 17283248640
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.
252 : 1, 2, 3, 4, 6, 7, 9, 12, 14, 18, 21, 28, 36, 42, 63, 84, 126, 252
378 : 1, 2, 3, 6, 7, 9, 14, 18, 21, 27, 42, 54, 63, 126, 189, 378
504 : 1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 18, 21, 24, 28, 36, 42, 56, 63, 72, 84, 126, 168, 252, 504
360 : 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180, 360
18 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 252,378,504,360, is 18.
Now, the common factors can be found like this.
252:2x 2x 3x 3x 7
378:2x 3x 3x 3x 7
504:2x 2x 2x 3x 3x 7
360:2x 2x 2x 3x 3x 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 3x 3x 3x 3x 7x 7 = 127008
Therefore, the value for common factors is 127008.
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 = 17283248640/(18x127008)
LCM = 17283248640/2286144
LCM = 7560
Thus, we can understand that the LCM of 252,378,504,360 is 7560.
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FAQs on LCM of 252, 378, 504, 360
1. What is the LCM of 252, 378, 504, 360?
Answer: LCM of 252, 378, 504, 360 is 7560.
2. How to calculate the LCM of 252, 378, 504, 360?
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 252, 378, 504, 360.
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}.