LCM of 742, 706, 364, 288
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 742, 706, 364, 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 742, 706, 364, 288. So, keep reading to learn more.
Given numbers are 742,706,364,288
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 742,706,364,288 is 490325472.
Find LCM of 742,706,364,288 with Prime Factorization
| 2 | 742, 706, 364, 288 |
| 2 | 371, 353, 182, 144 |
| 7 | 371, 353, 91, 72 |
| 53, 353, 13, 72 |
Multiply the prime numbers at the bottom and the left side.
2 x 2 x 7 x 53 x 353 x 13 x 72 = 490325472
Therefore, the lowest common multiple of 742,706,364,288 is 490325472.
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.
742 x 706 x 364 x 288 = 54916452864
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.
742 : 1, 2, 7, 14, 53, 106, 371, 742
706 : 1, 2, 353, 706
364 : 1, 2, 4, 7, 13, 14, 26, 28, 52, 91, 182, 364
288 : 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 72, 96, 144, 288
2 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 742,706,364,288, is 2.
Now, the common factors can be found like this.
742:2x 7x 53
706:2x 353
364:2x 2x 7x 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 7 = 56
Therefore, the value for common factors is 56.
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 = 54916452864/(2x56)
LCM = 54916452864/112
LCM = 490325472
Thus, we can understand that the LCM of 742,706,364,288 is 490325472.
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FAQs on LCM of 742, 706, 364, 288
1. What is the LCM of 742, 706, 364, 288?
Answer: LCM of 742, 706, 364, 288 is 490325472.
2. How to calculate the LCM of 742, 706, 364, 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 742, 706, 364, 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}.