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 320,564,420
We can find the LCD of numbers 320,564,420 by the prime factorization method or by applying the LCD formula.
The LCD of 320,564,420 is 315840.
Method to Find Least Common Denominator of 320,564,420 with Prime Factorization
| 2 | 320, 564, 420 |
| 2 | 160, 282, 210 |
| 3 | 80, 141, 105 |
| 5 | 80, 47, 35 |
| 16, 47, 7 |
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 16 x 47 x 7 = 315840
Thus, we have determined that the LCD of 320,564,420 is 315840
The LCD formula is LCD(a,b) = ( a x b) / GCF(a,b)
Step1:
Find the GCF of 320 and 564. To find the GCF, list down the factors of 320 and 564 and select the highest factor that appears in both lists of factors.
320 : [1, 2, 4, 5, 8, 10, 16, 20, 32, 40, 64, 80, 160, 320]
564 : [1, 2, 3, 4, 6, 12, 47, 94, 141, 188, 282, 564]
From this, we can see that the GCF of 320 and 564 is 4.
Now, put this into the LCD formula.
LCD(320, 564) = ( 320 x 564 ) / 4
LCD(320, 564) = 180480 / 4
LCD(320, 564) = 45120
Step2:
Find the GCF of 45120 and 420. To find the GCF, list down the factors of 45120 and 420 and select the highest factor that appears in both lists of factors.
45120 : [1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40, 47, 48, 60, 64, 80, 94, 96, 120, 141, 160, 188, 192, 235, 240, 282, 320, 376, 470, 480, 564, 705, 752, 940, 960, 1128, 1410, 1504, 1880, 2256, 2820, 3008, 3760, 4512, 5640, 7520, 9024, 11280, 15040, 22560, 45120]
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]
From this, we can see that the GCF of 45120 and 420 is 60.
Now, put this into the LCD formula.
LCD(45120, 420) = ( 45120 x 420 ) / 60
LCD(45120, 420) = 18950400 / 60
LCD(45120, 420) = 315840
LCD of 320,564,420 is 315840
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 .