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

- Find all the
**Factors**of each number, - Circle the
**Common**factors, - 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.**

- 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; - 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; - Divide the numbers inside the
**L sign**by the common factor and write the quotients under the corresponding numbers; - 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;
- Find the GCF and LCM based on the numbers on the outside of the ladder (Left side common factor and the final quotients):
**GCF = Multiply all of the numbers on the left side of the ladder (all common factors)****LCM = Multiply all of the numbers outside of the ladder (all common factors, and final quotients)**

Here is some good reading materials for your reference:

https://www.thatquiz.org/tq/previewtest?3/R/F/G/TO6B1395151998

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:

- Introduce Fraction
- Simplify a Fraction using GCF
- Change two fractions to the same denominator using LCM

Thanks

P.