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Example: Solve Linear Equation Involving Fractions

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Least common multiple

In arithmetic and number theory, the least common multiple (also called the lowest common multiple or smallest common multiple) of two integers a and b, usually denoted by LCM (a, b), is the smallest positive integer that is a multiple of both a and b. (Our solved example in mathguru.com uses this concept)

It is familiar from grade-school arithmetic as the "lowest common denominator" that must be determined before two fractions can be added.

If either a or b is 0, LCM (ab) is defined to be zero.

The LCM of more than two integers or rational numbers is well-defined: it is the smallest number that is an integer multiple of each of them.



What is the LCM of 4 and 6?

Multiples of 4 are:

4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60, 64, 68, 72, 76...

and the multiples of 6 are:

6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72, ...

Common multiples of 4 and 6 are simply the numbers that are in both lists:

12, 24, 36, 48, 60, 72, ....

So the least common multiple of 4 and 6 is the smallest one of those: 12 (Our solved example in mathguru.com uses this concept)





An equation is a mathematical statement that asserts the equality of two expressions. Equations consist of the expressions that have to be equal on opposite sides of an equal sign, as in



If an equation in algebra is known to be true, the following operations may be used to produce another true equation:

1.  Any real number can be added to both sides.

2.  Any real number can be subtracted from both sides.

3.  Any real number can be multiplied to both sides.

4.  Any non-zero real number can divide both sides. (Our solved example in mathguru.com uses this concept)



The above explanation is copied from Wikipedia, the free encyclopedia and is remixed as allowed under the Creative Commons Attribution- ShareAlike 3.0 Unported License.