LCM of 144, 420, 978, 564
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 144, 420, 978, 564 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 144, 420, 978, 564. So, keep reading to learn more.
Given numbers are 144,420,978,564
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 144,420,978,564 is 38611440.
Find LCM of 144,420,978,564 with Prime Factorization
| 2 | 144, 420, 978, 564 |
| 2 | 72, 210, 489, 282 |
| 3 | 36, 105, 489, 141 |
| 12, 35, 163, 47 |
Multiply the prime numbers at the bottom and the left side.
2 x 2 x 3 x 12 x 35 x 163 x 47 = 38611440
Therefore, the lowest common multiple of 144,420,978,564 is 38611440.
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.
144 x 420 x 978 x 564 = 33360284160
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.
144 : 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144
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
978 : 1, 2, 3, 6, 163, 326, 489, 978
564 : 1, 2, 3, 4, 6, 12, 47, 94, 141, 188, 282, 564
6 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 144,420,978,564, is 6.
Now, the common factors can be found like this.
144:2x 2x 2x 2x 3x 3
420:2x 2x 3x 5x 7
978:2x 3x 163
564:2x 2x 3x 47
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 3 = 144
Therefore, the value for common factors is 144.
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 = 33360284160/(6x144)
LCM = 33360284160/864
LCM = 38611440
Thus, we can understand that the LCM of 144,420,978,564 is 38611440.
LCM of two or more Numbers Calculation Examples
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FAQs on LCM of 144, 420, 978, 564
1. What is the LCM of 144, 420, 978, 564?
Answer: LCM of 144, 420, 978, 564 is 38611440.
2. How to calculate the LCM of 144, 420, 978, 564?
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 144, 420, 978, 564.
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}.