LCM of 972, 249, 456, 284
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 972, 249, 456, 284 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, 249, 456, 284. So, keep reading to learn more.
Given numbers are 972,249,456,284
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 972,249,456,284 is 217663848.
Find LCM of 972,249,456,284 with Prime Factorization
| 2 | 972, 249, 456, 284 |
| 2 | 486, 249, 228, 142 |
| 3 | 243, 249, 114, 71 |
| 81, 83, 38, 71 |
Multiply the prime numbers at the bottom and the left side.
2 x 2 x 3 x 81 x 83 x 38 x 71 = 217663848
Therefore, the lowest common multiple of 972,249,456,284 is 217663848.
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 249 x 456 x 284 = 31343594112
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
249 : 1, 3, 83, 249
456 : 1, 2, 3, 4, 6, 8, 12, 19, 24, 38, 57, 76, 114, 152, 228, 456
284 : 1, 2, 4, 71, 142, 284
1 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 972,249,456,284, is 1.
Now, the common factors can be found like this.
972:2x 2x 3x 3x 3x 3x 3
249:3x 83
456:2x 2x 2x 3x 19
284:2x 2x 71
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 3x 3 = 144
Therefore, the value for common factors is 144.
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 = 31343594112/(1x144)
LCM = 31343594112/144
LCM = 217663848
Thus, we can understand that the LCM of 972,249,456,284 is 217663848.
LCM of two or more Numbers Calculation Examples
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FAQs on LCM of 972, 249, 456, 284
1. What is the LCM of 972, 249, 456, 284?
Answer: LCM of 972, 249, 456, 284 is 217663848.
2. How to calculate the LCM of 972, 249, 456, 284?
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, 249, 456, 284.
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}.