LCM of 380, 456, 978, 174
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 380, 456, 978, 174 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 380, 456, 978, 174. So, keep reading to learn more.
Given numbers are 380,456,978,174
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 380,456,978,174 is 10777560.
Find LCM of 380,456,978,174 with Prime Factorization
| 2 | 380, 456, 978, 174 |
| 2 | 190, 228, 489, 87 |
| 3 | 95, 114, 489, 87 |
| 19 | 95, 38, 163, 29 |
| 5, 2, 163, 29 |
Multiply the prime numbers at the bottom and the left side.
2 x 2 x 3 x 19 x 5 x 2 x 163 x 29 = 10777560
Therefore, the lowest common multiple of 380,456,978,174 is 10777560.
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.
380 x 456 x 978 x 174 = 29487404160
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.
380 : 1, 2, 4, 5, 10, 19, 20, 38, 76, 95, 190, 380
456 : 1, 2, 3, 4, 6, 8, 12, 19, 24, 38, 57, 76, 114, 152, 228, 456
978 : 1, 2, 3, 6, 163, 326, 489, 978
174 : 1, 2, 3, 6, 29, 58, 87, 174
2 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 380,456,978,174, is 2.
Now, the common factors can be found like this.
380:2x 2x 5x 19
456:2x 2x 2x 3x 19
978:2x 3x 163
174:2x 3x 29
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 19 = 1368
Therefore, the value for common factors is 1368.
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 = 29487404160/(2x1368)
LCM = 29487404160/2736
LCM = 10777560
Thus, we can understand that the LCM of 380,456,978,174 is 10777560.
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FAQs on LCM of 380, 456, 978, 174
1. What is the LCM of 380, 456, 978, 174?
Answer: LCM of 380, 456, 978, 174 is 10777560.
2. How to calculate the LCM of 380, 456, 978, 174?
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 380, 456, 978, 174.
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}.