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21 May, 21:34

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

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  1. 22 May, 01:06
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    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
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