LCM of 314, 692, 234, 450, 420
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 314, 692, 234, 450, 420 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 314, 692, 234, 450, 420. So, keep reading to learn more.
Given numbers are 314,692,234,450,420
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 314,692,234,450,420 is 2224485900.
Find LCM of 314,692,234,450,420 with Prime Factorization
| 2 | 314, 692, 234, 450, 420 |
| 2 | 157, 346, 117, 225, 210 |
| 3 | 157, 173, 117, 225, 105 |
| 3 | 157, 173, 39, 75, 35 |
| 5 | 157, 173, 13, 25, 35 |
| 157, 173, 13, 5, 7 |
Multiply the prime numbers at the bottom and the left side.
2 x 2 x 3 x 3 x 5 x 157 x 173 x 13 x 5 x 7 = 2224485900
Therefore, the lowest common multiple of 314,692,234,450,420 is 2224485900.
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.
314 x 692 x 234 x 450 x 420 = 9609779088000
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.
314 : 1, 2, 157, 314
692 : 1, 2, 4, 173, 346, 692
234 : 1, 2, 3, 6, 9, 13, 18, 26, 39, 78, 117, 234
450 : 1, 2, 3, 5, 6, 9, 10, 15, 18, 25, 30, 45, 50, 75, 90, 150, 225, 450
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
2 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 314,692,234,450,420, is 2.
Now, the common factors can be found like this.
314:2x 157
692:2x 2x 173
234:2x 3x 3x 13
450:2x 3x 3x 5x 5
420:2x 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 2x 3x 3x 3x 5 = 2160
Therefore, the value for common factors is 2160.
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 = 9609779088000/(2x2160)
LCM = 9609779088000/4320
LCM = 2224485900
Thus, we can understand that the LCM of 314,692,234,450,420 is 2224485900.
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FAQs on LCM of 314, 692, 234, 450, 420
1. What is the LCM of 314, 692, 234, 450, 420?
Answer: LCM of 314, 692, 234, 450, 420 is 2224485900.
2. How to calculate the LCM of 314, 692, 234, 450, 420?
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 314, 692, 234, 450, 420.
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}.