Lesson Vocabulary

• complex fraction

Problem 1 Finding the Least Common Multiple

What is the LCM of 12 x 2 y ( x 2 + 2 x + 1 ) 12 x squared , y open , x squared , plus 2 x plus 1 close  and 18 x y 3 ( x 2 + 5 x + 4 ) ? 18 , x y cubed , open , x squared , plus 5 x plus 4 close question mark

• Step 1 Find the prime factors of each expression.

  12 x 2 y ( x 2 + 2 x + 1 ) = 2 2 · 3 x 2 y ( x + 1 ) 2 12 , x squared , y open , x squared , plus 2 x plus 1 close equals , 2 squared , middle dot , 3 x squared , y . open x plus 1 close squared

  18 x y 3 ( x 2 + 5 x + 4 ) = 2 · 3 2 x y 3 ( x + 1 ) ( x + 4 ) 18 . x y cubed , open , x squared , plus 5 x plus 4 close equals 2 middle dot , 3 squared . x y cubed , open x plus 1 close open x plus 4 close

• Step 2 Write the product of the prime factors, each raised to the greatest power that occurs in either expression.

  2 2 · 3 2 x 2 y 3 ( x + 1 ) 2 ( x + 4 ) 2 squared , middle dot , 3 squared , x squared , y cubed . open x plus 1 close squared . open x plus 4 close

The LCM is 2 2 · 3 2 x 2 y 3 ( x + 1 ) 2 ( x + 4 ) , or  36 x 2 y 3 ( x + 1 ) 2 ( x + 4 ) . 2 squared , middle dot , 3 squared , x squared , y cubed . open x plus 1 close squared . open x plus 4 close comma or . 36 x squared . y cubed . open x plus 1 close squared . open x plus 4 close .