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 840,315,728
We can find the LCD of numbers 840,315,728 by the prime factorization method or by applying the LCD formula.
The LCD of 840,315,728 is 32760.
Method to Find Least Common Denominator of 840,315,728 with Prime Factorization
| 2 | 840, 315, 728 |
| 2 | 420, 315, 364 |
| 2 | 210, 315, 182 |
| 3 | 105, 315, 91 |
| 5 | 35, 105, 91 |
| 7 | 7, 21, 91 |
| 1, 3, 13 |
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 2 x 3 x 5 x 7 x 1 x 3 x 13 = 32760
Thus, we have determined that the LCD of 840,315,728 is 32760
The LCD formula is LCD(a,b) = ( a x b) / GCF(a,b)
Step1:
Find the GCF of 840 and 315. To find the GCF, list down the factors of 840 and 315 and select the highest factor that appears in both lists of factors.
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]
315 : [1, 3, 5, 7, 9, 15, 21, 35, 45, 63, 105, 315]
From this, we can see that the GCF of 840 and 315 is 105.
Now, put this into the LCD formula.
LCD(840, 315) = ( 840 x 315 ) / 105
LCD(840, 315) = 264600 / 105
LCD(840, 315) = 2520
Step2:
Find the GCF of 2520 and 728. To find the GCF, list down the factors of 2520 and 728 and select the highest factor that appears in both lists of factors.
2520 : [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 15, 18, 20, 21, 24, 28, 30, 35, 36, 40, 42, 45, 56, 60, 63, 70, 72, 84, 90, 105, 120, 126, 140, 168, 180, 210, 252, 280, 315, 360, 420, 504, 630, 840, 1260, 2520]
728 : [1, 2, 4, 7, 8, 13, 14, 26, 28, 52, 56, 91, 104, 182, 364, 728]
From this, we can see that the GCF of 2520 and 728 is 56.
Now, put this into the LCD formula.
LCD(2520, 728) = ( 2520 x 728 ) / 56
LCD(2520, 728) = 1834560 / 56
LCD(2520, 728) = 32760
LCD of 840,315,728 is 32760
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 .