Question

Kira and Jake are building towers

Each one of Kira's blocks is 9 cm
tall. Each one of Jake's blocks is
12 cm tall.
They both build towers that are
exactly the same height. What is
the smallest height that their
towers could be? Give your answer in cm

Answer 1

The smallest height at which Kira and Jake's towers could be exactly the same is the Least Common Multiple (LCM) of the two block sizes, which is 36 cm.

Step-by-step explanation:

The student is asking about the smallest height at which two towers made of differently sized blocks, one set 9 cm tall and the other 12 cm tall, could be exactly the same height. This question involves finding the Least Common Multiple (LCM) of the two block sizes. We want to find the smallest whole number that is a multiple of both 9 cm and 12 cm.

To calculate the LCM of 9 and 12, we list the multiples of each:

• Multiples of 9: 9, 18, 27, 36, 45, 54, 63, 72, ...
• Multiples of 12: 12, 24, 36, 48, 60, 72, ...

The smallest common multiple is 36. Therefore, the smallest height at which Kira and Jake's towers could be exactly the same is 36 cm.