Lowest Common Denominator - Middle School Instruction

Middle School Instruction

Some K–1 math standards such as the latest revision of the NCTM math standards and reform mathematics textbooks created since the 1990s de-emphasize or omit coverage of the LCD entirely in favor of finding any common, but not necessarily the lowest common denominator, or by using less powerful methods such as fraction strips or "benchmark" fractions. The "cross-multiply" method of comparing fractions effectively creates a common denominator by multiplying both denominators together.

Algorithm finds lowest common denominator.

Lowest common denominator for 2/9 + 1/4 + 1/6:

Start with the 3 denominators in an upside-down division box. The algorithm uses similar division boxes going downward.

Start with 2 and see if it divides exactly into any of the three denominators. Then go to 3, then 5, then 7, and so on through prime numbers.

|_9_4_6_ 2|_9_4_6_ 2 doesn't go into 9 exactly. 2 goes into 4, leaving 2, and into 6, leaving 3. 2|_9_2_3_ 2 goes into 2, leaving 1. 3|_9_1_3_ 3 is the next divisor. 3 goes into 9, leaving 3, and into 3, leaving 1. 3|_3_1_1_ 3 goes into 3, leaving 1. |_1_1_1_

The process is to keep dividing the denominators until they reduce to 1. Then ignore the 1's and use the column of divisors as factors which produce the L.C.D.

2 x 2 x 3 x 3 = 36 = L.C.D.