LCD of Calculator
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Read this article to figure out how to calculate the lowest common denominator of . Learn the two different methods that you can use to find the LCD: the prime factorization method and the LCD formula method. We will explain both these methods in detail so stick around until the very end to understand. Utilise our free LCD Calculator to avail the LCD of numbers easily.
Given numbers are 810,780,840
We can find the LCD of numbers 810,780,840 by the prime factorization method or by applying the LCD formula.
The LCD of 810,780,840 is 294840.
Method to Find Least Common Denominator of 810,780,840 with Prime Factorization
| 2 | 810, 780, 840 |
| 2 | 405, 390, 420 |
| 3 | 405, 195, 210 |
| 5 | 135, 65, 70 |
| 27, 13, 14 |
As you can see, now we have to multiply the prime numbers on the left side with the co-primes at the bottom.
2 x 2 x 3 x 5 x 27 x 13 x 14 = 294840
Thus, we have determined that the LCD of 810,780,840 is 294840
The LCD formula is LCD(a,b) = ( a x b) / GCF(a,b)
Step1:
Find the GCF of 810 and 780. To find the GCF, list down the factors of 810 and 780 and select the highest factor that appears in both lists of factors.
810 : [1, 2, 3, 5, 6, 9, 10, 15, 18, 27, 30, 45, 54, 81, 90, 135, 162, 270, 405, 810]
780 : [1, 2, 3, 4, 5, 6, 10, 12, 13, 15, 20, 26, 30, 39, 52, 60, 65, 78, 130, 156, 195, 260, 390, 780]
From this, we can see that the GCF of 810 and 780 is 30.
Now, put this into the LCD formula.
LCD(810, 780) = ( 810 x 780 ) / 30
LCD(810, 780) = 631800 / 30
LCD(810, 780) = 21060
Step2:
Find the GCF of 21060 and 840. To find the GCF, list down the factors of 21060 and 840 and select the highest factor that appears in both lists of factors.
21060 : [1, 2, 3, 4, 5, 6, 9, 10, 12, 13, 15, 18, 20, 26, 27, 30, 36, 39, 45, 52, 54, 60, 65, 78, 81, 90, 108, 117, 130, 135, 156, 162, 180, 195, 234, 260, 270, 324, 351, 390, 405, 468, 540, 585, 702, 780, 810, 1053, 1170, 1404, 1620, 1755, 2106, 2340, 3510, 4212, 5265, 7020, 10530, 21060]
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]
From this, we can see that the GCF of 21060 and 840 is 60.
Now, put this into the LCD formula.
LCD(21060, 840) = ( 21060 x 840 ) / 60
LCD(21060, 840) = 17690400 / 60
LCD(21060, 840) = 294840
LCD of 810,780,840 is 294840
LCD of Numbers Calculation Examples
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Frequently Asked Questions on LCD of
1. What is the LCD of ?
Answer: LCD of is .
2. How to find LCD of using prime factorization ?
Answer: Just keep dividing by prime numbers until only co-primes are left over. At that point, simply multiply the co-primes with the prime numbers on the left. The answer will be , the LCD.
3. How to Find the LCD of using LCD formula ?
Answer: The LCD formula is LCD(a,b) = ( a x b) / GCF(a,b).
You must first calculate the LCD OF and . Then, find the LCD of that answer and and so on. The answer will be , which is the LCD of .