Here's another example to show why finding simplest common multiple saves you time.

1/xyz + 2/yzw

If you simply multiply the denominators to get xyzyzw as common denominator, you would work it this way.

= (1/xyz * yzw/yzw) + (2/yzw * xyz/xyz)

= yzw/xyzyzw + 2xyz/xyzyzw

= (yzw + 2xyz)/xyyzzw

But then you would see that yz is a factor of each term in the numerator. Use the distributive property to express this as a multiplication.

= yz(w + 2x)/xyyzzw

Now the factor yz in numerator and factor yz in denominator cancel. You can cancel because y and z here are factors in numerator and factors in denominator, no longer part of a sum.

= ~~yz~~(w + 2x)/xy~~yz~~zw

= (w + 2x)/xyzw

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If you instead think about LCM of fractions, and extend that idea to finding simplest common multiple of the denominators:

The original denominators xyz and yzw have xyzw as their simplest common multiple. You multiply each fraction by a version of 1 that will create the common multiple as the new denominator. (So multiply first fraction by w/w, and multiply second fraction by x/x.)

1/xyz + 2/yzw

= (1/xyz * w/w) + (2/yzw * x/x)

= w/xyzw + 2x/xyzw

= (w + 2x)/xyzw

This takes less writing, but a little more thinking up front to find the common denominator that is best to use.