Answered

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The bookstore sells packages of 15 pens
each and 12 pencils each. They want the
same number of pens and pencils in their
next order. Find the smallest number of
packages of each they can buy.

Sagot :

CintiaSalazar

Considering the definition of least common multiple, this means that smallest number of packages of each they can buy is 60.

Least common multiple

A number is a multiple of another when it contains it exactly n times. In other words, the multiples of a number are the ones you get when you multiply one number by another.

The least common multiple allows us to know what is the smallest number that is a multiple of a certain set of numbers.

One procedure for calculating the least common multiple is to break each number into prime factors. Then the common and uncommon factors are raised to the highest exponent, which must be multiplied.

Smallest number of packages

To calculate the smallest number of packages of each they can buy, you calculate the least common multiple.

First, the decomposition of the numbers into prime factors is carried out:

15= 3×5

12= 2×2×3= 2²×3

Then, the least common multiple is calculated as 2²×3×5

Solving, the least common multiple between 12 and 15 is 60.

Finally, this means that smallest number of packages of each they can buy is 60.

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