maths: Lowest common multiple

Hot dogs are sold in packages of 12 while hot dog buns are sold in packages of 8. Help me! Don't know what to do!

(a) How many packs of each should you buy to have the same number of hot dogs and hot dog buns?

(b) How many hot dogs in buns would you have?

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  1. what is the smallest number which is a multiple of both 8 and 12?

    8 = 2*2*2
    12 = 2*2*3

    so, an multiple of 8 must have 2 as a factor at least 3 times.
    Similarly, multiples of 12 have at least two 2's and one 3.

    So, pick the highest power of all the prime factors of each number:

    2^3 * 3 = 24

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  2. you even titled your post as "Lowest common multiple", so clearly that suggests the way to do it

    12 = 2x2x3
    8 = 2x2x2
    so we need 2x2x2x3 or 24 if every factor is to be included.

    no you need 24/12 or 2 packs of wieners, and
    you need 24/8 or 3 packs of buns

    notice 2x12= 24 wieners
    and 3x8 - 24 buns, you have enough buns for the wieners.

    another way to look at it:
    multiples of 12:
    12, 24, 36, 48, ...
    multiples of 8:
    8 , 16, 24, 32, ....

    ahhh 24 is the first number common to both.

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  3. Mrs. Cook wants to give each of her 24 students the same amount of candy. If each package of candy has 36 pieces in it, how many packages of candy should she buy so that there will be none left over?

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  4. I need help on this one to pleas.

    Mrs. Cook wants to give each of her 24 students the same amount of candy. If each package of candy has 36 pieces in it, how many packages of candy should she buy so that there will be none left over?

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  5. At a store, hot dogs come in a package of eight and hot dog buns come in a package of twelve. What is the least number of packages of each type that you can buy and have no hot dogs or buns left over?

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  6. uHHHhhHhHhHhHHHhhhhhhhhhhhhhHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHh

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