# What is the LCM and GCF of the numbers 16 and 40?

The least common multiple of 16 and 40 = 80

The smallest positive integer that is divisible by both numbers.

Other names include,

Lowest common multiple =80

Smallest common multiple = 80

The greatest common factor of 16 and 40 = 8

The Greatest Common Factor is the largest positive integer that will divide into the numbers with zero remainder.

Other names include,

The Greatest Common Divisor (GCD) 16 and 40 = 8

Highest Common Factor (HCF) 16 and 40 = 8

I use a factor tree and a chart in order to find the LCM and the GCF.

Once you have the prime factors for the LCM multiply all the factors together but if you have two of the same factor only use it once.

For the (GCF) find factors that you have pairs of the factors.

If you have multiple factors, multiply them together.

If you don't have pairs the (GCF) is 1.

If you have 3 numbers, for the LCM bring down only 1 number if you have two or three numbers in a column, and you must have three numbers in the column for the GCF.

Find the LCM of 2-3-4 or more Numbers

# What is the LCM and the GCF of 20 30 and 15?

The least common multiple of 20-30-15 = 60

The smallest positive integer that is divisible by both numbers.

Other names include,

Lowest common multiple =60

Smallest common multiple = 60

The greatest common factor of 20-30-15 = 5

The Greatest Common Factor is the largest positive integer that will divide into the numbers with zero remainder.

Other names include,

The Greatest Common Divisor (GCD) 20-30-15 = 60

Highest Common Factor (HCF) 20-30-15 = 5

I use a factor tree and a chart in order to find the LCM and the GCF.

Once you have the prime factors for the LCM multiply all the factors together but if you have two of the same factor only use it once.

For the (GCF) find factors that you have pairs of the factors.

If you have multiple factors, multiply them together.

If you don't have pairs the (GCF) is 1.

If you have 3 numbers, for the LCM bring down only 1 number if you have two or three numbers in a column, and you must have three numbers in the column for the GCF.

# Extract DNA from a Banana

In this lab you will get the opportunity to see what DNA actually looks like.
All items that you will need can be found at your local grocer.

Items you will need for the lab.
*Rubbing Alcohol
*Salt
*Banana
*Dish Detergent
*Two clear containers-Glass or plastic
*Spoon
*Cheesecloth
*Paper towels
* Plastic bags

Step 1. Place 1 tablespoon of salt,3 table spoons of water, and 1/2 of a banana in a plastic bag.

Step 2. Smash up the banana until it is has the texture of baby food.

Step 3. Strain the liquid from step 2 through the cheesecloth into a glass or cup.

Step 4. Gently stir in one table spoon of dish detergent.

Step 5. Pour in the rubbing alcohol down the side of the container. This allows the DNA to float to the surface.

If you have a microscope you can place the DNA on a slide and look at the DNA. I have completed this activity many times and I have found it has a very high success rate.
If you have any questions the video should be helpful.
You can also extract the DNA from strawberries.

# The Four Hemispheres of the Earth

The world is a very large place!  In order to find certain places on a map or globe, the world is divided into smaller sections to help locate certain places.

Let’s first take a look at the 4 Hemispheres.

The world can be divided in half, two different ways. First, you can divide the world into northern and southern halves.  The imaginary line that runs all the way around the world, which divides it into two equal halves, is called the equator. The equator is found at 0 degrees latitude. Any place above the equator is in the Northern Hemisphere. Any place below the equator is in the Southern Hemisphere.

The world can also be divided in half another way, separating east from west.  The imaginary line that divides the world into equal east and west halves is called the Prime Meridian and passes north to south through the Greenwich Observatory in London, England

The prime meridian is at 0° (0 degrees) longitude.

Any place to the left of the Prime Meridian is in the Western Hemisphere, while any place to the right of the Prime Meridian is in the Eastern Hemisphere.

Each of the seven continents is located in at least two hemispheres. The seven continents are,

Europe, Antarctica, Asia, Africa, Australia, North America, South America

An easy way to remember the 7 continents is to use

Eat An Aspirin After A Nighttime Snack

North America lies in the Western Hemisphere and the Northern Hemisphere.

There is only one continent in the world that lies in all four hemispheres: Africa.

As a result, Africa is the only continent to have land both at the Equator and the Prime Meridian.

# Quick tip to see if a number is prime

Which of these numbers are prime?

30,31,32,33,34,35,36,37,38,39,40

In this example 31 and 37 are prime.

A shortcut to see if a number is prime is to follow these rules.
Step 1. Find the square root of the number.
For example, the square root of 36 is 6.

Step 2. Find the prime factors of the square root.
For 6 = 2 and 3

Step 3. If the original number is divisible by these prime numbers then it is a composite number, if it is not divisible then it is prime.
36 is divisible by 2 and 3 so it is a composite number.

# What are cardinal directions and a compass rose?

Why? .... well let’s see.

Time for a road trip. Your directions say to start at the center of the 48 states near Lebanon Kansas. Then drive north until you reach the next border then turn and go west until you reach another border and then south to the middle of the next state.

Where do you end up?

In order to navigate these directions, you need to know your cardinal directions.

The cardinal directions are found on maps and compasses and can be found on a compass rose. Here is one example of a compass rose.

What are the different directions found on a compass rose?

An easy way to remember this is to use Never Eat Soggy Waffles

If you go in a clockwise manner you get North East South West

Between north and east, you can add northeast, between east and south you add southeast

Between south and west add southwest and final between west and north add northwest

These are intermediate measurements.

So Remember, Never eat those soggy waffles to stay on the correct path.

# LCM of 7 and 12 and GCF of 7 and 12

What is the LCM and GCF of 7 and 12?

The least common multiple of 7 and 12 = 84

The smallest positive integer that is divisible by both numbers.

Other names include,

Lowest common multiple =84

Smallest common multiple = 84

The greatest common factor of 7 and 12 = 1

The Greatest Common Factor is the largest positive integer that will divide into the numbers with zero remainder.

Other names include,

The Greatest Common Divisor (GCD) 7 and 12 = 1

Highest Common Factor (HCF) 7 and 12 = 1

I use a factor tree and a chart in order to find the LCM and the GCF.

Once you have the prime factors for the LCM multiply all the factors together but if you have two of the same factor only use it once.

For the (GCF) find factors that you have pairs of factors.

If you have multiple factors, multiply them together.

If you don't have pairs the (GCF) is 1.

If you have 3 numbers, for the LCM bring down only 1 number if you have two or three numbers in a column, and you must have three numbers in the column for the GCF.