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 270,406,378
We can find the LCD of numbers 270,406,378 by the prime factorization method or by applying the LCD formula.
The LCD of 270,406,378 is 54810.
Method to Find Least Common Denominator of 270,406,378 with Prime Factorization
| 2 | 270, 406, 378 |
| 3 | 135, 203, 189 |
| 3 | 45, 203, 63 |
| 3 | 15, 203, 21 |
| 7 | 5, 203, 7 |
| 5, 29, 1 |
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 3 x 3 x 3 x 7 x 5 x 29 x 1 = 54810
Thus, we have determined that the LCD of 270,406,378 is 54810
The LCD formula is LCD(a,b) = ( a x b) / GCF(a,b)
Step1:
Find the GCF of 270 and 406. To find the GCF, list down the factors of 270 and 406 and select the highest factor that appears in both lists of factors.
270 : [1, 2, 3, 5, 6, 9, 10, 15, 18, 27, 30, 45, 54, 90, 135, 270]
406 : [1, 2, 7, 14, 29, 58, 203, 406]
From this, we can see that the GCF of 270 and 406 is 2.
Now, put this into the LCD formula.
LCD(270, 406) = ( 270 x 406 ) / 2
LCD(270, 406) = 109620 / 2
LCD(270, 406) = 54810
Step2:
Find the GCF of 54810 and 378. To find the GCF, list down the factors of 54810 and 378 and select the highest factor that appears in both lists of factors.
54810 : [1, 2, 3, 5, 6, 7, 9, 10, 14, 15, 18, 21, 27, 29, 30, 35, 42, 45, 54, 58, 63, 70, 87, 90, 105, 126, 135, 145, 174, 189, 203, 210, 261, 270, 290, 315, 378, 406, 435, 522, 609, 630, 783, 870, 945, 1015, 1218, 1305, 1566, 1827, 1890, 2030, 2610, 3045, 3654, 3915, 5481, 6090, 7830, 9135, 10962, 18270, 27405, 54810]
378 : [1, 2, 3, 6, 7, 9, 14, 18, 21, 27, 42, 54, 63, 126, 189, 378]
From this, we can see that the GCF of 54810 and 378 is 378.
Now, put this into the LCD formula.
LCD(54810, 378) = ( 54810 x 378 ) / 378
LCD(54810, 378) = 20718180 / 378
LCD(54810, 378) = 54810
LCD of 270,406,378 is 54810
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 .