LCM of 120, 402, 546, 407, 768
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 120, 402, 546, 407, 768 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 120, 402, 546, 407, 768. So, keep reading to learn more.
Given numbers are 120,402,546,407,768
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 120,402,546,407,768 is 9528879360.
Find LCM of 120,402,546,407,768 with Prime Factorization
| 2 | 120, 402, 546, 407, 768 |
| 2 | 60, 201, 273, 407, 384 |
| 2 | 30, 201, 273, 407, 192 |
| 3 | 15, 201, 273, 407, 96 |
| 5, 67, 91, 407, 32 |
Multiply the prime numbers at the bottom and the left side.
2 x 2 x 2 x 3 x 5 x 67 x 91 x 407 x 32 = 9528879360
Therefore, the lowest common multiple of 120,402,546,407,768 is 9528879360.
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.
120 x 402 x 546 x 407 x 768 = 8232951767040
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.
120 : 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120
402 : 1, 2, 3, 6, 67, 134, 201, 402
546 : 1, 2, 3, 6, 7, 13, 14, 21, 26, 39, 42, 78, 91, 182, 273, 546
407 : 1, 11, 37, 407
768 : 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 128, 192, 256, 384, 768
1 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 120,402,546,407,768, is 1.
Now, the common factors can be found like this.
120:2x 2x 2x 3x 5
402:2x 3x 67
546:2x 3x 7x 13
407:11x 37
768:2x 2x 2x 2x 2x 2x 2x 2x 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 2x 3x 3x 3 = 864
Therefore, the value for common factors is 864.
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 = 8232951767040/(1x864)
LCM = 8232951767040/864
LCM = 9528879360
Thus, we can understand that the LCM of 120,402,546,407,768 is 9528879360.
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FAQs on LCM of 120, 402, 546, 407, 768
1. What is the LCM of 120, 402, 546, 407, 768?
Answer: LCM of 120, 402, 546, 407, 768 is 9528879360.
2. How to calculate the LCM of 120, 402, 546, 407, 768?
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 120, 402, 546, 407, 768.
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}.