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Solution
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Solution provided by AtoZmath.com
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LCD of fractions calculator
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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 9,12,15Method-1 : Finding LCM of 9,12,15 using Division MethodStep-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 LCMLCM of `9,12,15=2 xx 2 xx 3 xx 3 xx 5=180`
Method-2 : Finding LCM of 9,12,15 using Prime Factorization MethodStep-1: Prime factorization of `9,12,15` using factor by division method 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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