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At a local bakery, Edgar decorated $6$ cakes at a time. Javier decorated $8$ at a time. If they ended up decorating the same number of cakes by the end of the day, what is the smallest number of cakes that each must have decorated? $\newline$ $\newline$ _____cakes

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GCF and LCM: word problems

Full solution

Q. At a local bakery, Edgar decorated

6

cakes at a time. Javier decorated

8

at a time. If they ended up decorating the same number of cakes by the end of the day, what is the smallest number of cakes that each must have decorated?

\newline

\newline

_____cakes

Identify Concept: Identify the mathematical concept needed to solve the problem. We need to find the smallest number of cakes that both Edgar and Javier could have decorated, which means finding the Least Common Multiple (LCM) of the numbers of cakes they decorated at a time, $6$ and $8$ .
List Multiples: List the multiples of $6$ and $8$ to find the LCM. $\newline$ Multiples of $6$ : $6, 12, 18, 24, 30, 36, 42, 48\ldots$ $\newline$ Multiples of $8$ : $8, 16, 24, 32, 40, 48\ldots$ $\newline$ The smallest common multiple of $6$ and $8$ is $24$ .
Verify Calculation: Verify the calculation by checking if $24$ is divisible by both $6$ and $8$ . $\newline$ $24 \div 6 = 4$ $\newline$ $24 \div 8 = 3$ $\newline$ Both divisions result in whole numbers, confirming that $24$ is indeed the LCM.

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