a clockmacker must wind his clocks on a regular schedule. he winds some of his clock every three days and the remainder of his clocks every five days. how often does he wind all of his clocks on the same day? I need help with that problem
What time span do you need?
1, 4, 7, 10, 13, 16, 19, 22, 25, 28, 31
1, 6, 11, 16, 21, 26, 31
If he winds them all on day 1, he'll wind them all again on day 16 and day 31.
So he winds "some" of his clocks on day
3,6,9,12,15,18,...
He winds the remainder of the clocks on day
5,10,15,20,...
mmmh?
thank you both so much. I feel positive about using this website again.
You're very welcome.
To solve this problem, we can find the least common multiple (LCM) of 3 and 5. The LCM will give us the number of days after which the clockmaker will wind all of his clocks on the same day.
Step 1: Find the LCM of 3 and 5
Multiples of 3: 3, 6, 9, 12, 15, 18, ...
Multiples of 5: 5, 10, 15, 20, 25, 30, ...
The first common multiple of both 3 and 5 is 15. Therefore, the LCM of 3 and 5 is 15.
Step 2: Interpret the LCM
The LCM of 3 and 5 tells us that the clockmaker has to wait for 15 days before he winds all of his clocks on the same day.
So, the clockmaker will wind all of his clocks on the same day every 15 days.