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 420,560,504
We can find the LCD of numbers 420,560,504 by the prime factorization method or by applying the LCD formula.
The LCD of 420,560,504 is 5040.
Method to Find Least Common Denominator of 420,560,504 with Prime Factorization
| 2 | 420, 560, 504 |
| 2 | 210, 280, 252 |
| 2 | 105, 140, 126 |
| 3 | 105, 70, 63 |
| 5 | 35, 70, 21 |
| 7 | 7, 14, 21 |
| 1, 2, 3 |
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 2 x 3 = 5040
Thus, we have determined that the LCD of 420,560,504 is 5040
The LCD formula is LCD(a,b) = ( a x b) / GCF(a,b)
Step1:
Find the GCF of 420 and 560. To find the GCF, list down the factors of 420 and 560 and select the highest factor that appears in both lists of factors.
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]
560 : [1, 2, 4, 5, 7, 8, 10, 14, 16, 20, 28, 35, 40, 56, 70, 80, 112, 140, 280, 560]
From this, we can see that the GCF of 420 and 560 is 140.
Now, put this into the LCD formula.
LCD(420, 560) = ( 420 x 560 ) / 140
LCD(420, 560) = 235200 / 140
LCD(420, 560) = 1680
Step2:
Find the GCF of 1680 and 504. To find the GCF, list down the factors of 1680 and 504 and select the highest factor that appears in both lists of factors.
1680 : [1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 16, 20, 21, 24, 28, 30, 35, 40, 42, 48, 56, 60, 70, 80, 84, 105, 112, 120, 140, 168, 210, 240, 280, 336, 420, 560, 840, 1680]
504 : [1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 18, 21, 24, 28, 36, 42, 56, 63, 72, 84, 126, 168, 252, 504]
From this, we can see that the GCF of 1680 and 504 is 168.
Now, put this into the LCD formula.
LCD(1680, 504) = ( 1680 x 504 ) / 168
LCD(1680, 504) = 846720 / 168
LCD(1680, 504) = 5040
LCD of 420,560,504 is 5040
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 .