Mateo and Ivy are building towers made of blocks. Mateo is building a tower 9 blocks at a time, and Ivy is building a tower 15 blocks at a time. How many blocks high do both of their towers need to be for them to be the same height?(1 point)
Responses
45 blocks
90 blocks
30 blocks
54 blocks
The height of Mateo's tower is a multiple of 9, and the height of Ivy's tower is a multiple of 15. To find the height of the tower where they are the same height, we need to find the least common multiple (LCM) of 9 and 15.
The prime factors of 9 are 3^2 and the prime factors of 15 are 3 * 5. To find the LCM, we take the highest power of each prime factor that appears in either number. Therefore, the LCM of 9 and 15 is 3^2 * 5 = 45.
Therefore, both towers need to be 45 blocks high.