LCM of 972, 338, 414, 513
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 972, 338, 414, 513 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 972, 338, 414, 513. So, keep reading to learn more.
Given numbers are 972,338,414,513
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 972,338,414,513 is 71785116.
Find LCM of 972,338,414,513 with Prime Factorization
| 2 | 972, 338, 414, 513 |
| 3 | 486, 169, 207, 513 |
| 3 | 162, 169, 69, 171 |
| 3 | 54, 169, 23, 57 |
| 18, 169, 23, 19 |
Multiply the prime numbers at the bottom and the left side.
2 x 3 x 3 x 3 x 18 x 169 x 23 x 19 = 71785116
Therefore, the lowest common multiple of 972,338,414,513 is 71785116.
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.
972 x 338 x 414 x 513 = 69775132752
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.
972 : 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 81, 108, 162, 243, 324, 486, 972
338 : 1, 2, 13, 26, 169, 338
414 : 1, 2, 3, 6, 9, 18, 23, 46, 69, 138, 207, 414
513 : 1, 3, 9, 19, 27, 57, 171, 513
1 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 972,338,414,513, is 1.
Now, the common factors can be found like this.
972:2x 2x 3x 3x 3x 3x 3
338:2x 13x 13
414:2x 3x 3x 23
513:3x 3x 3x 19
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 3x 3x 3x 3x 3 = 972
Therefore, the value for common factors is 972.
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 = 69775132752/(1x972)
LCM = 69775132752/972
LCM = 71785116
Thus, we can understand that the LCM of 972,338,414,513 is 71785116.
LCM of two or more Numbers Calculation Examples
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FAQs on LCM of 972, 338, 414, 513
1. What is the LCM of 972, 338, 414, 513?
Answer: LCM of 972, 338, 414, 513 is 71785116.
2. How to calculate the LCM of 972, 338, 414, 513?
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 972, 338, 414, 513.
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}.