LCM of 840, 975, 321, 342
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 840, 975, 321, 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 840, 975, 321, 342. So, keep reading to learn more.
Given numbers are 840,975,321,342
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 840,975,321,342 is 333005400.
Find LCM of 840,975,321,342 with Prime Factorization
| 2 | 840, 975, 321, 342 |
| 3 | 420, 975, 321, 171 |
| 5 | 140, 325, 107, 57 |
| 28, 65, 107, 57 |
Multiply the prime numbers at the bottom and the left side.
2 x 3 x 5 x 28 x 65 x 107 x 57 = 333005400
Therefore, the lowest common multiple of 840,975,321,342 is 333005400.
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.
840 x 975 x 321 x 342 = 89911458000
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.
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
975 : 1, 3, 5, 13, 15, 25, 39, 65, 75, 195, 325, 975
321 : 1, 3, 107, 321
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 840,975,321,342, is 3.
Now, the common factors can be found like this.
840:2x 2x 2x 3x 5x 7
975:3x 5x 5x 13
321:3x 107
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 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 = 89911458000/(3x90)
LCM = 89911458000/270
LCM = 333005400
Thus, we can understand that the LCM of 840,975,321,342 is 333005400.
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FAQs on LCM of 840, 975, 321, 342
1. What is the LCM of 840, 975, 321, 342?
Answer: LCM of 840, 975, 321, 342 is 333005400.
2. How to calculate the LCM of 840, 975, 321, 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 840, 975, 321, 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}.