Common Denominators

1. Greatest Common Divisor (GCD) - Its the largest number that divides all respective numbers without a remainder.
2. Lowest Common Multiple (LCM) - Its the smallest common multiple of all respective number. It's also the smallest possible number that can be divided by all respective numbers without a remainder.

Factors of a number?

Factors of a number refer to all multiplication tables where the required number comes up. It means, the factor can be multiplied N number of times to reach that number.

Example - Factors of 12 are 1, 2, 3, 4, 6, 12. It means, 12 appears in the multiplication tables of all of these numbers.

GCD is nothing but that taking factors of two numbers and we take the largest number that appears in factors list of those two numbers. The number can be divided each of it's factors and the remainder will be zero. This is why it's called the greatest common divisor.

LCM is the actual opposite of GCD

• GCD is the largest common number that divides a set of numbers. Example, GCD(12, 24) is 12. Because 12 divides the numbers without remainder. Also it's the greatest. Even 2 is a valid value but it's not the greatest.
• LCM is the lowest common number that arrives when we check the multiples of the numbers in set. Example, LCM(12 and 24), value is 24 is the least/lowest value that comes we you see the tables of 12 and 24.

In division, GCD is the divisor that returns no remainder where as, LCD is the dividend that returns no remainder

Lowest Common Denominator and Least Common Multiple

Least common multiple is the original concept.

LCD is one of the applications of LCM when applied for fractions. When we want to add two fractions of different denominators, we must push them to a value of LCD so that additional can be performed.

When LCD comes up, always think about LCM and it's full form. Then the core meaning immediately strikes and then it becomes easy to understand whats LCD.

using LCD as a metaphor

We use LCD as a Metaphor to describe whats really whats the least common thing. This refers to using or having something that's common or applies to everyone in the set.

Applications of GCD

When we've two groups of different sizes, then we can use GCD to divide two groups into equal sub groups. Divide 36 apples and 48 oranges into the largest possible equal groups. GCD is 12, so each group will have 12 items.

Understanding GCD geometrically

• When we've two lines of different lengths, GCD is about figuring out the largest size with which we can cut both lines into equal parts. If we've two lines of 48cm and 18cm, then we can split them into small sticks of 6cm without any remainder.

• When we've a rectangle floor, whats the largest possible square tiles that can be laid out without any space leftover.

Applications of LCM

LCM is used to determine when events that repeat at different intervals will coincide. If two traffic lights change every 12 and 18 seconds, they will coincide every 36 seconds (LCM of 12 and 18).