1. Find LCD of fractions of `8/9,35/12,7/15`

Solution:
Step-1 : `8/9,35/12,7/15`

Step-2 : Find the least common multiple (LCM) of denominators

Steps of LCM of 9,12,15

Method-1 : Finding LCM of 9,12,15 using Division Method
Step-1: Divide the numbers by prime factors until the remainder is 1

2	9		12		15
2	9		6		15
3	9		3		15
3	3		1		5
5	1		1		5
	1		1		1

Step-2: Multiply all the divisors to obtain the LCM

LCM of `9,12,15=2 xx 2 xx 3 xx 3 xx 5=180`

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Method-2 : Finding LCM of 9,12,15 using Prime Factorization Method
Step-1: Prime factorization of `9,12,15` using factor by division method

3 9 3 3   1

2 12 2 6 3 3   1

3 15 5 5   1

Step-2: Write each number as a product of primes, matching primes vertically when possible

9	=			3	× 3
12	=	2	× 2	× 3
15	=			3		× 5

Step-3: Bring down the primes in each column. The LCM is the product of these factors

9	=			3	× 3
12	=	2	× 2	× 3
15	=			3		× 5
LCM	=	2	× 2	× 3	× 3	× 5	= 180

`:.` LCM of `9,12,15` is `180`

Here, LCM of `9,12,15 = 180`

Step-3 :
`:.` LCD (Least common denominator) of `8/9,35/12,7/15` is `180`

Step-4 : Rewriting the original inputs as equivalent fractions with the LCD:
`8/9=8/9xx20/20=160/180`

`35/12=35/12xx15/15=525/180`

`7/15=7/15xx12/12=84/180`

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2. Find LCD of fractions of `1/2,2/3,3/4`

Solution:
Step-1 : `1/2,2/3,3/4`

Step-2 : Find the least common multiple (LCM) of denominators

Steps of LCM of 2,3,4

Method-1 : Finding LCM of 2,3,4 using Division Method
Step-1: Divide the numbers by prime factors until the remainder is 1

2	2		3		4
2	1		3		2
3	1		3		1
	1		1		1

Step-2: Multiply all the divisors to obtain the LCM

LCM of `2,3,4=2 xx 2 xx 3=12`

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Method-2 : Finding LCM of 2,3,4 using Prime Factorization Method
Step-1: Prime factorization of `2,3,4` using factor by division method

2 2   1

3 3   1

2 4 2 2   1

Step-2: Write each number as a product of primes, matching primes vertically when possible

2	=	2
3	=			3
4	=	2	× 2

Step-3: Bring down the primes in each column. The LCM is the product of these factors

2	=	2
3	=			3
4	=	2	× 2
LCM	=	2	× 2	× 3	= 12

`:.` LCM of `2,3,4` is `12`

Here, LCM of `2,3,4 = 12`

Step-3 :
`:.` LCD (Least common denominator) of `1/2,2/3,3/4` is `12`

Step-4 : Rewriting the original inputs as equivalent fractions with the LCD:
`1/2=1/2xx6/6=6/12`

`2/3=2/3xx4/4=8/12`

`3/4=3/4xx3/3=9/12`

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3. Find LCD of fractions of `5/4,3/2,7/5`

Solution:
Step-1 : `5/4,3/2,7/5`

Step-2 : Find the least common multiple (LCM) of denominators

Steps of LCM of 4,2,5

Method-1 : Finding LCM of 4,2,5 using Division Method
Step-1: Divide the numbers by prime factors until the remainder is 1

2	4		2		5
2	2		1		5
5	1		1		5
	1		1		1

Step-2: Multiply all the divisors to obtain the LCM

LCM of `4,2,5=2 xx 2 xx 5=20`

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Method-2 : Finding LCM of 4,2,5 using Prime Factorization Method
Step-1: Prime factorization of `4,2,5` using factor by division method

2 4 2 2   1

2 2   1

5 5   1

Step-2: Write each number as a product of primes, matching primes vertically when possible

4	=	2	× 2
2	=	2
5	=			5

Step-3: Bring down the primes in each column. The LCM is the product of these factors

4	=	2	× 2
2	=	2
5	=			5
LCM	=	2	× 2	× 5	= 20

`:.` LCM of `4,2,5` is `20`

Here, LCM of `4,2,5 = 20`

Step-3 :
`:.` LCD (Least common denominator) of `5/4,3/2,7/5` is `20`

Step-4 : Rewriting the original inputs as equivalent fractions with the LCD:
`5/4=5/4xx5/5=25/20`

`3/2=3/2xx10/10=30/20`

`7/5=7/5xx4/4=28/20`

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