How Do You Find The Equivalent Fractions Using Least Common Denominator LCD?

2/3, 1/2, 5/12
thanked the writer.
The least common multiple of two numbers is the smallest value that has each of the two numbers as a divisor.

Example
The least common multiple of 6 and 15 is 30. 6*5=30, 15*2=30

If we have two fractions, say 5/6 and 11/15, that we want to add, we need to express them as equivalent fractions having a common denominator. The least common multiple of the denominator values is called the Least Common Denominator (LCD).

Because we know the LCD of 6 and 15 is 30, we can express each of these fractions as something with a denominator of 30. Remember 6*5 = 30, and 15*2 = 30. We can use these facts to help form the equivalent fractions.

(5/6)*(5/5) = (5*5)/(6*5) = 25/30
(11/15)*(2/2) = (11*2)/(15*2) = 22/30

In each case, we have a fraction with a denominator d1, and we have a common denominator dc such that dc/d1 is an integer. We use this integer to make a fraction whose value is 1 = (dc/d1)/(dc/d1). Then we multiply our original fraction by that to get its equivalent with a denominator of dc.

Example
Our fraction is 11/15. The LCD is 30. Our multiplier value is 30/15 = 2, and the fraction that we multiply by is 1 = 2/2, like this:
(11/15)*(2/2) = (11*2)/(15*2) = 22/30

22/30 is an equivalent fraction to 11/15. We used the LCD of 30 to determine what the equivalent fraction should be.

thanked the writer.
If you have the fractions, per say
1/4 & 2/7
you would find the least common denominator (LCD)  In this case it would be 28.
You would then write down the LCD (28) and fine out what you multiply each to get that number.
1/4 = ?/28 - 28 / 4 = 7 ~ 1 * 7 = 7 | 7/28
2/7 = ?/28 - 28 / 7 = 4 ~ 2 * 4 = 8 | 8/28
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Using 24 as the denominator what is equivalent to 1/2
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