Least Common Multiple

Finding the Least of the Most

Melanie Anderson

Least Common Multiple

• A Multiple of a number is the product of the number and any whole number. – Example: number x number = product (multiple)

• When you count by twos, fives or tens, you are using multiples.

• 2: 2, 4, 6, 8, 10, 12 multiples of two• 4: 4, 8, 12, 16, 20 multiples of four• 5: 5, 10, 15, 20, 25 multiples of five

Least Common MultipleMultiples of 6

1 x 6 = 62 x 6 = 123 x 6 = 184 x 6 = 245 x 6 = 306 x 6 = 367 x 6 = 42

Multiples of 71 x 7 = 72 x 7 = 143 x 7 = 214 x 7 = 285 x 7 = 356 x 7 = 42

The answer or product is the multiple. To help you find the LCM make a list of the multiples of the number then draw circle around the number that is the same.

42 is the lowest number that is the same in both list, 42 is the LCM

The Least Common Multiple or the LCM is the lowest number you get when you compare the multiples of numbers.

Ex. 1: Find the LCM of 10 and 30

10: 10, 20, 30, 40, 5030: 30, 60, 90

So the LCM is 30 because 30 is the lowest number in the list of multiples

Ex. 2: Find the LCM of 12 and 18

12: 12, 24, 36, 4818: 18, 36, 54

So the LCM is 36 because 36 is the lowest number in the list of multiples.

Least Common Multiple

• Ex.3 Find the LCM of 5 and 7Multiples of 5 are 5, 10, 15, 20, 25, 30, 35, 40Multiples of 7 are 7, 14, 21, 28, 35, 42

Can you find the multiple? The lowest number that is the same in both list.

The answer is 35. SOOOO the LCM is 35!!! Easy right!!

How to use LCM?

When you are looking for a pattern?Example: Ikisha has piano lessons every 3rd day and swim lessons every 4th of the month. On what days will she have both piano and swim lessons?First look for a pattern or the LCM of both numbers.Multiples of 33, 6, 9, 12, 15, 18, 21, 24, 27, 30Multiples of 44, 8, 12, 16, 20, 24, 28Circle the lowest common numberAnswer: on the 12th day Ikisha willhave both piano and swim lessons.

1 2 3 4 5 6 7

8 9 10 11 12 13 14

15 16 17 18 19 20 21

22 23 24 25 26 27 28

29 30 31

How to use LCM?When you are finding a common denominator to add or subtract fractions? This is called a LCM for least common denominator.Notice the denominators are not the same. Use the multiples of 4 and 2 to find the LCM.Multiples of 4: 4, 8

Multiples of 2: 2, 4, 6 4 is the LCM or LCD ¼ + ½ = To make the denominators the same, you multiply.

1 + 1 x 2 =2 1 + 2 = 34 2 x 2 =4 4 4 4

Do not change 1/4

Now the denominators

are alike.Notice the

numerator and denominator are multiplied by 2

Least Common Multiple

Points to remember!!1. A multiple is the product of two numbers.2. List the multiples of each number to find the

common number.3. Use LCM to find patterns.4. Use LCM to add or subtract fractions, the

LCM becomes the LCD (the least common denominator).