LCM of 342, 504, 508, 688, 735
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 342, 504, 508, 688, 735 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 342, 504, 508, 688, 735. So, keep reading to learn more.
Given numbers are 342,504,508,688,735
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 342,504,508,688,735 is 3660617520.
Find LCM of 342,504,508,688,735 with Prime Factorization
| 2 | 342, 504, 508, 688, 735 |
| 2 | 171, 252, 254, 344, 735 |
| 2 | 171, 126, 127, 172, 735 |
| 3 | 171, 63, 127, 86, 735 |
| 3 | 57, 21, 127, 86, 245 |
| 7 | 19, 7, 127, 86, 245 |
| 19, 1, 127, 86, 35 |
Multiply the prime numbers at the bottom and the left side.
2 x 2 x 2 x 3 x 3 x 7 x 19 x 1 x 127 x 86 x 35 = 3660617520
Therefore, the lowest common multiple of 342,504,508,688,735 is 3660617520.
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.
342 x 504 x 508 x 688 x 735 = 44278829521920
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.
342 : 1, 2, 3, 6, 9, 18, 19, 38, 57, 114, 171, 342
504 : 1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 18, 21, 24, 28, 36, 42, 56, 63, 72, 84, 126, 168, 252, 504
508 : 1, 2, 4, 127, 254, 508
688 : 1, 2, 4, 8, 16, 43, 86, 172, 344, 688
735 : 1, 3, 5, 7, 15, 21, 35, 49, 105, 147, 245, 735
1 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 342,504,508,688,735, is 1.
Now, the common factors can be found like this.
342:2x 3x 3x 19
504:2x 2x 2x 3x 3x 7
508:2x 2x 127
688:2x 2x 2x 2x 43
735:3x 5x 7x 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 2x 2x 2x 2x 2x 3x 3x 3x 7 = 12096
Therefore, the value for common factors is 12096.
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 = 44278829521920/(1x12096)
LCM = 44278829521920/12096
LCM = 3660617520
Thus, we can understand that the LCM of 342,504,508,688,735 is 3660617520.
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FAQs on LCM of 342, 504, 508, 688, 735
1. What is the LCM of 342, 504, 508, 688, 735?
Answer: LCM of 342, 504, 508, 688, 735 is 3660617520.
2. How to calculate the LCM of 342, 504, 508, 688, 735?
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 342, 504, 508, 688, 735.
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}.