LCM of 708, 654, 120, 690
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 708, 654, 120, 690 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 708, 654, 120, 690. So, keep reading to learn more.
Given numbers are 708,654,120,690
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 708,654,120,690 is 17749560.
Find LCM of 708,654,120,690 with Prime Factorization
| 2 | 708, 654, 120, 690 |
| 2 | 354, 327, 60, 345 |
| 3 | 177, 327, 30, 345 |
| 5 | 59, 109, 10, 115 |
| 59, 109, 2, 23 |
Multiply the prime numbers at the bottom and the left side.
2 x 2 x 3 x 5 x 59 x 109 x 2 x 23 = 17749560
Therefore, the lowest common multiple of 708,654,120,690 is 17749560.
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.
708 x 654 x 120 x 690 = 38339049600
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.
708 : 1, 2, 3, 4, 6, 12, 59, 118, 177, 236, 354, 708
654 : 1, 2, 3, 6, 109, 218, 327, 654
120 : 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120
690 : 1, 2, 3, 5, 6, 10, 15, 23, 30, 46, 69, 115, 138, 230, 345, 690
6 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 708,654,120,690, is 6.
Now, the common factors can be found like this.
708:2x 2x 3x 59
654:2x 3x 109
120:2x 2x 2x 3x 5
690:2x 3x 5x 23
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 3x 3x 5 = 360
Therefore, the value for common factors is 360.
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 = 38339049600/(6x360)
LCM = 38339049600/2160
LCM = 17749560
Thus, we can understand that the LCM of 708,654,120,690 is 17749560.
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FAQs on LCM of 708, 654, 120, 690
1. What is the LCM of 708, 654, 120, 690?
Answer: LCM of 708, 654, 120, 690 is 17749560.
2. How to calculate the LCM of 708, 654, 120, 690?
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 708, 654, 120, 690.
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}.