LCM of 624, 135, 105, 252
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 624, 135, 105, 252 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 624, 135, 105, 252. So, keep reading to learn more.
Given numbers are 624,135,105,252
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 624,135,105,252 is 196560.
Find LCM of 624,135,105,252 with Prime Factorization
| 2 | 624, 135, 105, 252 |
| 2 | 312, 135, 105, 126 |
| 3 | 156, 135, 105, 63 |
| 3 | 52, 45, 35, 21 |
| 5 | 52, 15, 35, 7 |
| 7 | 52, 3, 7, 7 |
| 52, 3, 1, 1 |
Multiply the prime numbers at the bottom and the left side.
2 x 2 x 3 x 3 x 5 x 7 x 52 x 3 x 1 x 1 = 196560
Therefore, the lowest common multiple of 624,135,105,252 is 196560.
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.
624 x 135 x 105 x 252 = 2228990400
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.
624 : 1, 2, 3, 4, 6, 8, 12, 13, 16, 24, 26, 39, 48, 52, 78, 104, 156, 208, 312, 624
135 : 1, 3, 5, 9, 15, 27, 45, 135
105 : 1, 3, 5, 7, 15, 21, 35, 105
252 : 1, 2, 3, 4, 6, 7, 9, 12, 14, 18, 21, 28, 36, 42, 63, 84, 126, 252
3 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 624,135,105,252, is 3.
Now, the common factors can be found like this.
624:2x 2x 2x 2x 3x 13
135:3x 3x 3x 5
105:3x 5x 7
252:2x 2x 3x 3x 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 2x 3x 3x 3x 5x 7 = 3780
Therefore, the value for common factors is 3780.
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 = 2228990400/(3x3780)
LCM = 2228990400/11340
LCM = 196560
Thus, we can understand that the LCM of 624,135,105,252 is 196560.
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FAQs on LCM of 624, 135, 105, 252
1. What is the LCM of 624, 135, 105, 252?
Answer: LCM of 624, 135, 105, 252 is 196560.
2. How to calculate the LCM of 624, 135, 105, 252?
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 624, 135, 105, 252.
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}.