1. Find LCD of 12/25,18/45

Solution:
Step-1 : `12/25,18/45`

Step-2 : Find the least common multiple (LCM) of denominators
Here, LCM of `25,45 = 225`

Step-3 :
`:.` Least common denominator (LCD) of `25,45 = 225`

Step-4 : Rewriting the original inputs as equivalent fractions with the LCD:
`25/225,45/225`

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Steps of finding LCM of 25,45

Method-1 : Finding LCM of 25,45 using Division Method
Step-1: Divide the numbers by prime factors until the remainder is 1

3	25		45
3	25		15
5	25		5
5	5		1
	1		1

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

LCM of `25,45=3 xx 3 xx 5 xx 5=225`

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Method-2 : Finding LCM of 25,45 using Prime Factorization Method
Step-1: Prime factorization of `25,45` using factor by division method

5 25 5 5   1

3 45 3 15 5 5   1

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

25	=			5	× 5
45	=	3	× 3	× 5

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

25	=			5	× 5
45	=	3	× 3	× 5
LCM	=	3	× 3	× 5	× 5	= 225

`:.` LCM of `25,45` is `225`

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2. Find LCD of 8/9,32/12,10/15

Solution:
Step-1 : `8/9,32/12,10/15`

Step-2 : Find the least common multiple (LCM) of denominators
Here, LCM of `9,12,15 = 180`

Step-3 :
`:.` Least common denominator (LCD) of `9,12,15 = 180`

Step-4 : Rewriting the original inputs as equivalent fractions with the LCD:
`9/180,12/180,15/180`

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Steps of finding 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`

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3. Find LCD of 4/5,3/10,7/15

Solution:
Step-1 : `4/5,3/10,7/15`

Step-2 : Find the least common multiple (LCM) of denominators
Here, LCM of `5,10,15 = 30`

Step-3 :
`:.` Least common denominator (LCD) of `5,10,15 = 30`

Step-4 : Rewriting the original inputs as equivalent fractions with the LCD:
`5/30,10/30,15/30`

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Steps of finding LCM of 5,10,15

Method-1 : Finding LCM of 5,10,15 using Division Method
Step-1: Divide the numbers by prime factors until the remainder is 1

2	5		10		15
3	5		5		15
5	5		5		5
	1		1		1

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

LCM of `5,10,15=2 xx 3 xx 5=30`

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Method-2 : Finding LCM of 5,10,15 using Prime Factorization Method
Step-1: Prime factorization of `5,10,15` using factor by division method

5 5   1

2 10 5 5   1

3 15 5 5   1

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

5	=			5
10	=	2		× 5
15	=		3	× 5

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

5	=			5
10	=	2		× 5
15	=		3	× 5
LCM	=	2	× 3	× 5	= 30

`:.` LCM of `5,10,15` is `30`

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