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)”
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.
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 )
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:
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