LCM of 748, 312, 420, 108
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 748, 312, 420, 108 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 748, 312, 420, 108. So, keep reading to learn more.
Given numbers are 748,312,420,108
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 748,312,420,108 is 18378360.
Find LCM of 748,312,420,108 with Prime Factorization
| 2 | 748, 312, 420, 108 |
| 2 | 374, 156, 210, 54 |
| 3 | 187, 78, 105, 27 |
| 187, 26, 35, 9 |
Multiply the prime numbers at the bottom and the left side.
2 x 2 x 3 x 187 x 26 x 35 x 9 = 18378360
Therefore, the lowest common multiple of 748,312,420,108 is 18378360.
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.
748 x 312 x 420 x 108 = 10585935360
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.
748 : 1, 2, 4, 11, 17, 22, 34, 44, 68, 187, 374, 748
312 : 1, 2, 3, 4, 6, 8, 12, 13, 24, 26, 39, 52, 78, 104, 156, 312
420 : 1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 28, 30, 35, 42, 60, 70, 84, 105, 140, 210, 420
108 : 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 108
4 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 748,312,420,108, is 4.
Now, the common factors can be found like this.
748:2x 2x 11x 17
312:2x 2x 2x 3x 13
420:2x 2x 3x 5x 7
108:2x 2x 3x 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 2x 3x 3 = 144
Therefore, the value for common factors is 144.
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 = 10585935360/(4x144)
LCM = 10585935360/576
LCM = 18378360
Thus, we can understand that the LCM of 748,312,420,108 is 18378360.
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FAQs on LCM of 748, 312, 420, 108
1. What is the LCM of 748, 312, 420, 108?
Answer: LCM of 748, 312, 420, 108 is 18378360.
2. How to calculate the LCM of 748, 312, 420, 108?
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 748, 312, 420, 108.
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}.