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what is the common denominator for 23/72plus5/16plus8/63

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2 Answers

Write each number as product of its prime factors:
 
   72 = 23 . 32
   
    16 = 24
 
    63 = 32 .  7
                         
 
Lowest common Denominator : Product of common factors with highest exponent times uncommon factor.
 
LCD = 24 . 3 . 7 = 1008 

Comments

I am not sure students (possibly pre-algebra or algebra 1) looking for a common denominator will all know what prime factors are.  If so that's great and your way is more deterministic.
 
But Mike, if you haven't done prime factors just go at it more from a brute force method.
Prime factors are just doing division Tree in each number, and write them as exponents.
Do you want a common denominator?  Or a least common denominator?
 
You can always find a common denominator by multiplying the denominators together.
So  C.D. = 72 x 16 x 63
 
If you want a L.C.D. you will need to reduce it after.
If it is even you can always reduce by dividing by 2.
Keep doing that until you get an odd number or to the lowest even number you can that is still bigger than the largest denominator (in this case 63).
You can then try dividing by odd numbers until you can't find one any smaller that is bigger than the largest (63).
If you get an even number try dividing by 2s again.
Just remember it can't be any smaller than the largest (in this case 63).

Comments

I should have been more descriptive in case you didn't know just what I meant.
When you are looking for the lowest number above 16
that number must be divisible by each of the 3 numbers 16, 63, and 72