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 138,189,144
We can find the LCD of numbers 138,189,144 by the prime factorization method or by applying the LCD formula.
The LCD of 138,189,144 is 69552.
Method to Find Least Common Denominator of 138,189,144 with Prime Factorization
| 2 | 138, 189, 144 |
| 3 | 69, 189, 72 |
| 3 | 23, 63, 24 |
| 23, 21, 8 |
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 23 x 21 x 8 = 69552
Thus, we have determined that the LCD of 138,189,144 is 69552
The LCD formula is LCD(a,b) = ( a x b) / GCF(a,b)
Step1:
Find the GCF of 138 and 189. To find the GCF, list down the factors of 138 and 189 and select the highest factor that appears in both lists of factors.
138 : [1, 2, 3, 6, 23, 46, 69, 138]
189 : [1, 3, 7, 9, 21, 27, 63, 189]
From this, we can see that the GCF of 138 and 189 is 3.
Now, put this into the LCD formula.
LCD(138, 189) = ( 138 x 189 ) / 3
LCD(138, 189) = 26082 / 3
LCD(138, 189) = 8694
Step2:
Find the GCF of 8694 and 144. To find the GCF, list down the factors of 8694 and 144 and select the highest factor that appears in both lists of factors.
8694 : [1, 2, 3, 6, 7, 9, 14, 18, 21, 23, 27, 42, 46, 54, 63, 69, 126, 138, 161, 189, 207, 322, 378, 414, 483, 621, 966, 1242, 1449, 2898, 4347, 8694]
144 : [1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144]
From this, we can see that the GCF of 8694 and 144 is 18.
Now, put this into the LCD formula.
LCD(8694, 144) = ( 8694 x 144 ) / 18
LCD(8694, 144) = 1251936 / 18
LCD(8694, 144) = 69552
LCD of 138,189,144 is 69552
LCD of Numbers Calculation Examples
Here are some samples of LCD of Numbers calculations.
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 .