LCM of 291, 420, 735, 105
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 291, 420, 735, 105 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 291, 420, 735, 105. So, keep reading to learn more.
Given numbers are 291,420,735,105
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 291,420,735,105 is 285180.
Find LCM of 291,420,735,105 with Prime Factorization
| 3 | 291, 420, 735, 105 |
| 5 | 97, 140, 245, 35 |
| 7 | 97, 28, 49, 7 |
| 97, 4, 1, 7 |
Multiply the prime numbers at the bottom and the left side.
3 x 5 x 7 x 97 x 4 x 1 x 7 = 285180
Therefore, the lowest common multiple of 291,420,735,105 is 285180.
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.
291 x 420 x 735 x 105 = 9432328500
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.
291 : 1, 3, 97, 291
420 : 1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 28, 30, 35, 42, 60, 70, 84, 105, 140, 210, 420
735 : 1, 3, 5, 7, 15, 21, 35, 49, 105, 147, 245, 735
105 : 1, 3, 5, 7, 15, 21, 35, 105
3 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 291,420,735,105, is 3.
Now, the common factors can be found like this.
291:3x 97
420:2x 2x 3x 5x 7
735:3x 5x 7x 7
105:3x 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.
3x 3x 5x 5x 7x 7 = 11025
Therefore, the value for common factors is 11025.
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 = 9432328500/(3x11025)
LCM = 9432328500/33075
LCM = 285180
Thus, we can understand that the LCM of 291,420,735,105 is 285180.
LCM of two or more Numbers Calculation Examples
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FAQs on LCM of 291, 420, 735, 105
1. What is the LCM of 291, 420, 735, 105?
Answer: LCM of 291, 420, 735, 105 is 285180.
2. How to calculate the LCM of 291, 420, 735, 105?
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 291, 420, 735, 105.
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}.