LCM of 840, 249, 507, 288
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 840, 249, 507, 288 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 840, 249, 507, 288. So, keep reading to learn more.
Given numbers are 840,249,507,288
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 840,249,507,288 is 141392160.
Find LCM of 840,249,507,288 with Prime Factorization
| 2 | 840, 249, 507, 288 |
| 2 | 420, 249, 507, 144 |
| 2 | 210, 249, 507, 72 |
| 3 | 105, 249, 507, 36 |
| 35, 83, 169, 12 |
Multiply the prime numbers at the bottom and the left side.
2 x 2 x 2 x 3 x 35 x 83 x 169 x 12 = 141392160
Therefore, the lowest common multiple of 840,249,507,288 is 141392160.
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.
840 x 249 x 507 x 288 = 30540706560
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.
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
249 : 1, 3, 83, 249
507 : 1, 3, 13, 39, 169, 507
288 : 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 72, 96, 144, 288
3 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 840,249,507,288, is 3.
Now, the common factors can be found like this.
840:2x 2x 2x 3x 5x 7
249:3x 83
507:3x 13x 13
288:2x 2x 2x 2x 2x 3x 3
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 = 30540706560/(3x72)
LCM = 30540706560/216
LCM = 141392160
Thus, we can understand that the LCM of 840,249,507,288 is 141392160.
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FAQs on LCM of 840, 249, 507, 288
1. What is the LCM of 840, 249, 507, 288?
Answer: LCM of 840, 249, 507, 288 is 141392160.
2. How to calculate the LCM of 840, 249, 507, 288?
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 840, 249, 507, 288.
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}.