Question

Grocery Shopping: Hot dogs are sold in packages of 10, but hot dog buns come in packs of eight. What is the smallest number that makes the hot dogs and buns come out even?

Factors and multiples
ANSWERED
asked 2021-08-05
Grocery Shopping Hot dogs are sold in packages of 10, but hot dog buns come in packs of eight. What is the smallest number that makes the hot dogs and buns come out even?

Answers (1)

2021-08-06
Given information:
Given package of hot dogs contains hot dogs: 10.
Given package of hot dog buns contains buns: 8.
Concept used:
Least common multiple of two or more numbers is the smallest multiple that is completely divisible by the corresponding numbers leaving remainder zero. Least Common Multiple can be find by two methods - one by multiples method while other by prime factors method.
In prime factors method, we break the given numbers in terms of their prime factors and look out common factors. Then, we multiply the each of the common factor, number of times it occurs in factorization of any of the number and the factors that are not common. The product thus, obtained is the least common multiple of the given numbers.
Calculations:
We know thatleast common multiple of two or more numbers is the smallest multiple that is completely divisible by the corresponding numbers leaving remainder zero. Therefore, to find the smallest number that makes hot dogs and buns come out even, we need to find the least common multiple of number of hot dogs sold in a package and number of buns in a hot dog bun package.
According to question, the given pair of numbers are 10,8.
Using prime factors method, we have,
\(\displaystyle\Rightarrow{10}={2}\times{5}\)
\(\displaystyle\Rightarrow{8}={2}\times{2}\times{2}\)
From the above, we find that the common factor among factors of 10,8 is 2 and uncommon factors are 2,2 and 5. So, we have,
\(\displaystyle\Rightarrow{L}{C}{M}={2}\times{2}\times{2}\times{5}\) [Simplifying]
\(\displaystyle={40}\)
Hence, the smallest number that makes hot dogs and buns come out even is 40.
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