LCM of 120, 189, 112, 824
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 120, 189, 112, 824 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 120, 189, 112, 824. So, keep reading to learn more.
Given numbers are 120,189,112,824
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 120,189,112,824 is 1557360.
Find LCM of 120,189,112,824 with Prime Factorization
| 2 | 120, 189, 112, 824 |
| 2 | 60, 189, 56, 412 |
| 2 | 30, 189, 28, 206 |
| 3 | 15, 189, 14, 103 |
| 7 | 5, 63, 14, 103 |
| 5, 9, 2, 103 |
Multiply the prime numbers at the bottom and the left side.
2 x 2 x 2 x 3 x 7 x 5 x 9 x 2 x 103 = 1557360
Therefore, the lowest common multiple of 120,189,112,824 is 1557360.
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.
120 x 189 x 112 x 824 = 2093091840
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.
120 : 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120
189 : 1, 3, 7, 9, 21, 27, 63, 189
112 : 1, 2, 4, 7, 8, 14, 16, 28, 56, 112
824 : 1, 2, 4, 8, 103, 206, 412, 824
1 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 120,189,112,824, is 1.
Now, the common factors can be found like this.
120:2x 2x 2x 3x 5
189:3x 3x 3x 7
112:2x 2x 2x 2x 7
824:2x 2x 2x 103
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 2x 3x 7 = 1344
Therefore, the value for common factors is 1344.
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 = 2093091840/(1x1344)
LCM = 2093091840/1344
LCM = 1557360
Thus, we can understand that the LCM of 120,189,112,824 is 1557360.
LCM of two or more Numbers Calculation Examples
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FAQs on LCM of 120, 189, 112, 824
1. What is the LCM of 120, 189, 112, 824?
Answer: LCM of 120, 189, 112, 824 is 1557360.
2. How to calculate the LCM of 120, 189, 112, 824?
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 120, 189, 112, 824.
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}.