Math G6 Classroom 20160925

Hello All,

We learned two definitions in the class today: Greatest Common Factor (GCF) and Least Common Multiple (LCM) .

Greatest Common Factor (GCF)

The Greatest Common Factor (GCF) is the greatest number that is a common factor for each of two or more numbers. The “Greatest Common Factor” is also known as:
the “Greatest Common Divisor (GCD)”, or the “Highest Common Factor (HCF)”

For Example:

Greatest Common Factor of 12 and 16

  1. Find all the Factors of each number,
  2. Circle the Common factors,
  3. Choose the Greatest of those

Least Common Multiple (LCM)

The Least Common Multiple (LCM), is the smallest positive integer that is divisible by both a and b.

For Example:

Least Common Multiple of 3 and 5:

List the Multiples of each number,

The multiples of 3 are 3, 6, 9, 12, 15, 18, … etc
The multiples of 5 are 5, 10, 15, 20, 25, … etc

Find the first Common (same) value:

The Least Common Multiple of 3 and 5 is 15

( 15 is a common multiple of 3 and 5, and is the smallest, or least, common multiple )

Ladder Method

How to find the Greatest Common Factor (GCF) and the Least Common Multiple (LCM)? We introduce Short Division Method or Ladder Method.

  1. Write the numbers side by side with the L sign around. The L sign is the short division sign, which is used for doing a division;
  2. Try the common factor and write it on the left side of the L sign. Try initially the factors like 2/3/5/7/11/13/17 … … if you cannot think of the bigger one, it is good start;
  3. Divide the numbers inside the L sign by the common factor and write the quotients under the corresponding numbers;
  4. Try the common factor again till nothing goes into both of the quotients; it does means there is no more common factors for both numbers;
  5. Find the GCF and LCM based on the numbers on the outside of the ladder (Left side common factor and the final quotients):
    1. GCF = Multiply all of the numbers on the left side of the ladder (all common factors)
    2. LCM = Multiply all of the numbers outside of the ladder (all common factors, and final quotients)
Ladder Method for Finding GCF and LCM

Here is some good reading materials for your reference:

The Homework:

Please continue working on MathSmart 6 based on your schedule. If you haven’t finished the in-class practice, please finish that. Please work on the practice sheet in the email.

The Plan for the next class:

In the next class, we will go through:

  1. Introduce Fraction
  2. Simplify a Fraction using GCF
  3. Change two fractions to the same denominator using LCM




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