LCM of 309, 972, 216, 224
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 309, 972, 216, 224 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 309, 972, 216, 224. So, keep reading to learn more.
Given numbers are 309,972,216,224
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 309,972,216,224 is 5606496.
Find LCM of 309,972,216,224 with Prime Factorization
| 2 | 309, 972, 216, 224 |
| 2 | 309, 486, 108, 112 |
| 2 | 309, 243, 54, 56 |
| 3 | 309, 243, 27, 28 |
| 3 | 103, 81, 9, 28 |
| 3 | 103, 27, 3, 28 |
| 103, 9, 1, 28 |
Multiply the prime numbers at the bottom and the left side.
2 x 2 x 2 x 3 x 3 x 3 x 103 x 9 x 1 x 28 = 5606496
Therefore, the lowest common multiple of 309,972,216,224 is 5606496.
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.
309 x 972 x 216 x 224 = 14532037632
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.
309 : 1, 3, 103, 309
972 : 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 81, 108, 162, 243, 324, 486, 972
216 : 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 108, 216
224 : 1, 2, 4, 7, 8, 14, 16, 28, 32, 56, 112, 224
1 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 309,972,216,224, is 1.
Now, the common factors can be found like this.
309:3x 103
972:2x 2x 3x 3x 3x 3x 3
216:2x 2x 2x 3x 3x 3
224:2x 2x 2x 2x 2x 7
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 3x 3 = 2592
Therefore, the value for common factors is 2592.
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 = 14532037632/(1x2592)
LCM = 14532037632/2592
LCM = 5606496
Thus, we can understand that the LCM of 309,972,216,224 is 5606496.
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FAQs on LCM of 309, 972, 216, 224
1. What is the LCM of 309, 972, 216, 224?
Answer: LCM of 309, 972, 216, 224 is 5606496.
2. How to calculate the LCM of 309, 972, 216, 224?
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 309, 972, 216, 224.
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}.