If the brown rods (8 units) and the orange rods (10 units) are each used to form the shortest possible one-color train of matching length, how many brown rods and how many orange rods will be required?
What information about common factors or common multiples does this provide?
To find the shortest possible one-color train of matching length using the brown rods and orange rods, we need to find the least common multiple (LCM) of 8 and 10.
The multiples of 8 are: 8, 16, 24, 32, 40, 48, ...
The multiples of 10 are: 10, 20, 30, 40, 50, ...
The least common multiple of 8 and 10 is 40.
Therefore, to form the shortest possible one-color train of matching length, we would need 5 brown rods (8 x 5 = 40 units) and 4 orange rods (10 x 4 = 40 units).
This provides information about the common multiple of 8 and 10, which is 40. It also indicates that the greatest common factor of these two numbers is 2, as both numbers are even and divisible by 2.