Find one multiple less than 100 and one multiple greater than 100 that has 3, 11, and 22 as factors

A multiple less than 100 is 66

A multiple greater than 100 is 726

Step-by-step explanation:

* Lets explain how to solve the problem

- A multiple of a number is that number multiplied by an integer

# Ex: 10 is a multiple of 2 because 2 * 5 = 10

- The first multiple of a number is the number itself

- Factors of a number are the numbers you multiply to get the number

# Ex: the factors of 6 are 1, 2, 3, 6 because 6 = 1 * 6, 6 = 2 * 3

* Lets solve the problem

- The factors of the number are 3, 11, 22

- We can find a number has these factors by multiplying them

∵ The factors of the number are 3, 11, 22

∴ The number is = 3 * 11 * 22 = 726

- We need a multiple greater than 100

∵ 726 is greater than 100

∵ 726 has 3, 11, 22 as factors of it

∴ A multiple greater than 100 is 726

* Now we need multiple less than 100

- Lets find the factors of 3, 11, 22

∵ The factors of 3 are 1, 3 ⇒ (3 = 1 * 3)

∵ The factors of 11 are 1, 11 ⇒ (11 = 1 * 11)

∵ The factors of 22 are 1, 2, 11, 22 ⇒ (22 = 1 * 22, 22 = 2 * 11)

- To find the multiple we will chose its factors from the factors

of 3, 11, 22 without repeating the factor

∵ The factors of the multiple are 1, 2, 3, 11

# Note: We will not chose 22 because 2 * 11 = 22

∴ The multiple = 2 * 3 * 11 = 66

- We need a multiple less than 100

∵ 66 is less than 100

∵ 66 has 3, 11, 22 as factors of it

∴ A multiple less than 100 is 66