LCM of 414, 217, 157, 120
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 414, 217, 157, 120 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 414, 217, 157, 120. So, keep reading to learn more.
Given numbers are 414,217,157,120
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 414,217,157,120 is 282091320.
Find LCM of 414,217,157,120 with Prime Factorization
| 2 | 414, 217, 157, 120 |
| 3 | 207, 217, 157, 60 |
| 69, 217, 157, 20 |
Multiply the prime numbers at the bottom and the left side.
2 x 3 x 69 x 217 x 157 x 20 = 282091320
Therefore, the lowest common multiple of 414,217,157,120 is 282091320.
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.
414 x 217 x 157 x 120 = 1692547920
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.
414 : 1, 2, 3, 6, 9, 18, 23, 46, 69, 138, 207, 414
217 : 1, 7, 31, 217
157 : 1, 157
120 : 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120
1 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 414,217,157,120, is 1.
Now, the common factors can be found like this.
414:2x 3x 3x 23
217:7x 31
157:157
120:2x 2x 2x 3x 5
From this, we can see that the common factors because they appear for more than two numbers. So, just multiply them all together.
2x 3 = 6
Therefore, the value for common factors is 6.
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 = 1692547920/(1x6)
LCM = 1692547920/6
LCM = 282091320
Thus, we can understand that the LCM of 414,217,157,120 is 282091320.
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FAQs on LCM of 414, 217, 157, 120
1. What is the LCM of 414, 217, 157, 120?
Answer: LCM of 414, 217, 157, 120 is 282091320.
2. How to calculate the LCM of 414, 217, 157, 120?
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 414, 217, 157, 120.
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}.