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James’s four-year-old brother is trying to arrange black and yellow Legos in rows. He has 56 yellow Legos and 120 black Legos. He wants to arrange them in rows so that there are either only yellow or only black Legos in each row, and so that each row has the same number of Legos. What is the least number of rows he can make?

 Apr 19, 2020
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James’s four-year-old brother is trying to arrange black and yellow Legos in rows.
He has 56 yellow Legos and 120 black Legos.
He wants to arrange them in rows so that there are either only yellow or only black Legos in each row,
and so that each row has the same number of Legos.
What is the least number of rows he can make?

 

\(\begin{array}{|rcll|} \hline gcd(56,120) &=& 8 \\ \dfrac{56}{8} &=& 7 \\ \dfrac{120}{8} &=& 15 \\ \hline \end{array}\)

 

The least number of rows he can have is 22;

7 rows of yellow and 15 rows of black.

 

laugh

 Apr 20, 2020

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