Mario walks his dog once every 8 days in the park. Todd walks his dog once every 14 days. today, both Mario and Todd walked their dogs in the park. In how many more days will both boys walk their dogs in the park on the same day?
56
What is the least common multiple of 8 and 14?
To find out when Mario and Todd will walk their dogs in the park on the same day, we can find the least common multiple (LCM) of 8 and 14.
Prime factorization of 8: 2 × 2 × 2
Prime factorization of 14: 2 × 7
To find the LCM, we take the highest power of each prime factor:
LCM = 2³ × 7 = 56
Thus, Mario and Todd will walk their dogs in the park on the same day in 56 days.
To find out in how many more days both boys will walk their dogs in the park on the same day, we need to determine the least common multiple (LCM) of 8 and 14.
First, let's list out the multiples of 8 and 14 to find their common multiple:
Multiples of 8: 8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96, ...
Multiples of 14: 14, 28, 42, 56, 70, 84, 98, ...
From the lists, we can see that the first number they have in common is 56. Therefore, both boys will walk their dogs on the same day 56 days from today.
So, in 56 more days, both Mario and Todd will walk their dogs in the park on the same day.