LCM of 138, 165, 240, 342
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 138, 165, 240, 342 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 138, 165, 240, 342. So, keep reading to learn more.
Given numbers are 138,165,240,342
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 138,165,240,342 is 3461040.
Find LCM of 138,165,240,342 with Prime Factorization
| 2 | 138, 165, 240, 342 |
| 3 | 69, 165, 120, 171 |
| 5 | 23, 55, 40, 57 |
| 23, 11, 8, 57 |
Multiply the prime numbers at the bottom and the left side.
2 x 3 x 5 x 23 x 11 x 8 x 57 = 3461040
Therefore, the lowest common multiple of 138,165,240,342 is 3461040.
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.
138 x 165 x 240 x 342 = 1868961600
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.
138 : 1, 2, 3, 6, 23, 46, 69, 138
165 : 1, 3, 5, 11, 15, 33, 55, 165
240 : 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 40, 48, 60, 80, 120, 240
342 : 1, 2, 3, 6, 9, 18, 19, 38, 57, 114, 171, 342
3 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 138,165,240,342, is 3.
Now, the common factors can be found like this.
138:2x 3x 23
165:3x 5x 11
240:2x 2x 2x 2x 3x 5
342:2x 3x 3x 19
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 3x 3x 5 = 180
Therefore, the value for common factors is 180.
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 = 1868961600/(3x180)
LCM = 1868961600/540
LCM = 3461040
Thus, we can understand that the LCM of 138,165,240,342 is 3461040.
LCM of two or more Numbers Calculation Examples
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FAQs on LCM of 138, 165, 240, 342
1. What is the LCM of 138, 165, 240, 342?
Answer: LCM of 138, 165, 240, 342 is 3461040.
2. How to calculate the LCM of 138, 165, 240, 342?
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 138, 165, 240, 342.
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}.