LCM of 223, 784, 210, 300, 132
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 223, 784, 210, 300, 132 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 223, 784, 210, 300, 132. So, keep reading to learn more.
Given numbers are 223,784,210,300,132
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 223,784,210,300,132 is 144236400.
Find LCM of 223,784,210,300,132 with Prime Factorization
| 2 | 223, 784, 210, 300, 132 |
| 2 | 223, 392, 105, 150, 66 |
| 3 | 223, 196, 105, 75, 33 |
| 5 | 223, 196, 35, 25, 11 |
| 7 | 223, 196, 7, 5, 11 |
| 223, 28, 1, 5, 11 |
Multiply the prime numbers at the bottom and the left side.
2 x 2 x 3 x 5 x 7 x 223 x 28 x 1 x 5 x 11 = 144236400
Therefore, the lowest common multiple of 223,784,210,300,132 is 144236400.
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.
223 x 784 x 210 x 300 x 132 = 1453902912000
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.
223 : 1, 223
784 : 1, 2, 4, 7, 8, 14, 16, 28, 49, 56, 98, 112, 196, 392, 784
210 : 1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 30, 35, 42, 70, 105, 210
300 : 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 60, 75, 100, 150, 300
132 : 1, 2, 3, 4, 6, 11, 12, 22, 33, 44, 66, 132
1 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 223,784,210,300,132, is 1.
Now, the common factors can be found like this.
223:223
784:2x 2x 2x 2x 7x 7
210:2x 3x 5x 7
300:2x 2x 3x 5x 5
132:2x 2x 3x 11
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 5x 7 = 10080
Therefore, the value for common factors is 10080.
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 = 1453902912000/(1x10080)
LCM = 1453902912000/10080
LCM = 144236400
Thus, we can understand that the LCM of 223,784,210,300,132 is 144236400.
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FAQs on LCM of 223, 784, 210, 300, 132
1. What is the LCM of 223, 784, 210, 300, 132?
Answer: LCM of 223, 784, 210, 300, 132 is 144236400.
2. How to calculate the LCM of 223, 784, 210, 300, 132?
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 223, 784, 210, 300, 132.
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}.