Math Is Fun Forum

Techarena

Guest

How to find LCD

Hi All,

Help me to find out the least common denominator of 4/8, 6 / 10  and 9 / 18

Bob

Administrator

Registered: 2010-06-20

Posts: 10,643

Re: How to find LCD

hi Techarena

Welcome to the forum.

The denominators are 8, 10 and 18.

You are seeking a number that is a multiple of all three.  The slow way would be to list the multiples and just look for the first common one:

8, 16, 24, 32, 40, ......

10, 20, 30, 40, 50, .......

18, 36, 54, 72, 90, .......

When you get to a number that is all three lists, that's the common denominator.  If it's the first (lowest) then it's the least common denominator.

But here's a more efficient way:

Reduce each number to its prime factors:

8 = 2 x 2 x 2

10 = 2 x 5

18 = 2 x 3 x 3

To be a denominator for all three it must have everyone of those factors:

2 x 2 x 2 x 5 x 3 x 3 = 360.

So the fractions can be re-written as:

I was taught to think and simplify before jumping in with arithmetic, so if I was asked to add these fractions I would change the first and third into one half and cancel the middle one to 3/5.  Then I can add them in my head to get one and 3/5.

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob