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# Least Common Denominator

The Least Common Denominator (also called the Lowest Common Denominator, LCD) is the smallest number which is a multiple of two or more (numbers in the) denominators.

The LCD is a special case of the Least Common Multiple concept

Wow! Who did understand anything?

But wait! Don't you see?

That units matters and that you cannot add apples with oranges.

The LCD allows us to add fractions because we can work out a common ground for our arithmetical operation! All apples!

You can also consider this exercise to understand the concept.

2. The jewels in a crown (ratio problem) from my fraction worksheets webpage.

605. The student should read his author with the most sus-
tained attention, in order to discover the meaning of every sen-
tence. If the book is well written, it will endure and repay his
close attention: the text ought to be fairly intelligible, even
without illustrative examples. Often, far too often, a reader
hurries over the text without any sincere and vigorous effort to
understand it; and rushes to some example to clear up what
ought not to have been obscure, if it had been adequately con-
sidered. The habit of scrupulously investigating the text seems
to me important on several grounds. The close scrutiny of lan-
guage is a very valuable exercise both for studious and practical
life. In the higher departments of mathematics the habit is
indispensable: in the long investigations which occur there it
would be impossible to interpose illustrative examples at every
stage, the student must therefore encounter and master, sen-
tence by sentence, an extensive and complicated argument.

TODHUNTER, ISAAC.

Source: Memorabilia mathematica; or, The philomath's quotation-book - Moritz, Robert Édouard, 1868-1940

From the least common denominator (LCD) back to homepage

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