LCM of 74, 42, 75, 42, 840
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 74, 42, 75, 42, 840 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 74, 42, 75, 42, 840. So, keep reading to learn more.
Given numbers are 74,42,75,42,840
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 74,42,75,42,840 is 155400.
Find LCM of 74,42,75,42,840 with Prime Factorization
| 2 | 74, 42, 75, 42, 840 |
| 3 | 37, 21, 75, 21, 420 |
| 5 | 37, 7, 25, 7, 140 |
| 7 | 37, 7, 5, 7, 28 |
| 37, 1, 5, 1, 4 |
Multiply the prime numbers at the bottom and the left side.
2 x 3 x 5 x 7 x 37 x 1 x 5 x 1 x 4 = 155400
Therefore, the lowest common multiple of 74,42,75,42,840 is 155400.
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.
74 x 42 x 75 x 42 x 840 = 8223768000
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.
74 : 1, 2, 37, 74
42 : 1, 2, 3, 6, 7, 14, 21, 42
75 : 1, 3, 5, 15, 25, 75
42 : 1, 2, 3, 6, 7, 14, 21, 42
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
1 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 74,42,75,42,840, is 1.
Now, the common factors can be found like this.
74:2x 37
42:2x 3x 7
75:3x 5x 5
42:2x 3x 7
840:2x 2x 2x 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.
2x 2x 2x 3x 3x 3x 5x 7x 7 = 52920
Therefore, the value for common factors is 52920.
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 = 8223768000/(1x52920)
LCM = 8223768000/52920
LCM = 155400
Thus, we can understand that the LCM of 74,42,75,42,840 is 155400.
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FAQs on LCM of 74, 42, 75, 42, 840
1. What is the LCM of 74, 42, 75, 42, 840?
Answer: LCM of 74, 42, 75, 42, 840 is 155400.
2. How to calculate the LCM of 74, 42, 75, 42, 840?
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 74, 42, 75, 42, 840.
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}.