LCM of 369, 690, 723, 840
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 369, 690, 723, 840 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 369, 690, 723, 840. So, keep reading to learn more.
Given numbers are 369,690,723,840
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 369,690,723,840 is 572702760.
Find LCM of 369,690,723,840 with Prime Factorization
| 2 | 369, 690, 723, 840 |
| 3 | 369, 345, 723, 420 |
| 5 | 123, 115, 241, 140 |
| 123, 23, 241, 28 |
Multiply the prime numbers at the bottom and the left side.
2 x 3 x 5 x 123 x 23 x 241 x 28 = 572702760
Therefore, the lowest common multiple of 369,690,723,840 is 572702760.
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.
369 x 690 x 723 x 840 = 154629745200
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.
369 : 1, 3, 9, 41, 123, 369
690 : 1, 2, 3, 5, 6, 10, 15, 23, 30, 46, 69, 115, 138, 230, 345, 690
723 : 1, 3, 241, 723
840 : 1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 20, 21, 24, 28, 30, 35, 40, 42, 56, 60, 70, 84, 105, 120, 140, 168, 210, 280, 420, 840
3 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 369,690,723,840, is 3.
Now, the common factors can be found like this.
369:3x 3x 41
690:2x 3x 5x 23
723:3x 241
840:2x 2x 2x 3x 5x 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 3x 3x 5 = 90
Therefore, the value for common factors is 90.
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 = 154629745200/(3x90)
LCM = 154629745200/270
LCM = 572702760
Thus, we can understand that the LCM of 369,690,723,840 is 572702760.
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FAQs on LCM of 369, 690, 723, 840
1. What is the LCM of 369, 690, 723, 840?
Answer: LCM of 369, 690, 723, 840 is 572702760.
2. How to calculate the LCM of 369, 690, 723, 840?
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 369, 690, 723, 840.
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}.