LCM of 420, 596, 144, 667, 138
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 420, 596, 144, 667, 138 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 420, 596, 144, 667, 138. So, keep reading to learn more.
Given numbers are 420,596,144,667,138
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 420,596,144,667,138 is 500890320.
Find LCM of 420,596,144,667,138 with Prime Factorization
| 2 | 420, 596, 144, 667, 138 |
| 2 | 210, 298, 72, 667, 69 |
| 3 | 105, 149, 36, 667, 69 |
| 23 | 35, 149, 12, 667, 23 |
| 35, 149, 12, 29, 1 |
Multiply the prime numbers at the bottom and the left side.
2 x 2 x 3 x 23 x 35 x 149 x 12 x 29 x 1 = 500890320
Therefore, the lowest common multiple of 420,596,144,667,138 is 500890320.
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.
420 x 596 x 144 x 667 x 138 = 3317897479680
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.
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
596 : 1, 2, 4, 149, 298, 596
144 : 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144
667 : 1, 23, 29, 667
138 : 1, 2, 3, 6, 23, 46, 69, 138
1 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 420,596,144,667,138, is 1.
Now, the common factors can be found like this.
420:2x 2x 3x 5x 7
596:2x 2x 149
144:2x 2x 2x 2x 3x 3
667:23x 29
138:2x 3x 23
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 23 = 6624
Therefore, the value for common factors is 6624.
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 = 3317897479680/(1x6624)
LCM = 3317897479680/6624
LCM = 500890320
Thus, we can understand that the LCM of 420,596,144,667,138 is 500890320.
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FAQs on LCM of 420, 596, 144, 667, 138
1. What is the LCM of 420, 596, 144, 667, 138?
Answer: LCM of 420, 596, 144, 667, 138 is 500890320.
2. How to calculate the LCM of 420, 596, 144, 667, 138?
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 420, 596, 144, 667, 138.
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}.