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?

Question

Mathematics

Grady Kelly

14 November, 08:24

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?

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Answers (1)

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Lindsay Lloyd · Answer 1

The least number of rows he can have is 22; 7 rows of yellow and 15 rows of black.

We find the GCF of both numbers to determine how many Legos will be in each row. Find the prime factorization of both numbers:

56 = 7 (2) (2) (2)

120 = 3 (5) (2) (2) (2)

The GCF is 2 (2) (2) = 8. This means there will be 8 Legos in each row.

For the yellow Legos, 56/8 = 7 rows.

For the black Legos, 120/8 = 15 rows.

This gives us 7+15=22 rows.