A bell rings every 10 minutes and a buzzer sounds every 15 minutes they were both heard at 2nd clock
When would they both be heard next?
What is the least common multiple of 10 and 15?
2.30
To find out when the bell and buzzer will be heard next at the same time, we need to find the least common multiple (LCM) of 10 and 15.
Step 1: Find the multiples of each number:
Multiples of 10: 10, 20, 30, 40, 50, 60, 70, 80, 90, ...
Multiples of 15: 15, 30, 45, 60, 75, 90, ...
Step 2: Identify the common multiples:
The common multiples of 10 and 15 are 30, 60, 90, ...
Step 3: Determine the next occurrence after the 2nd clock:
Since the multiples of 10 and 15 are increasing, we need to find the next occurrence after the 2nd clock.
The 2nd clock is at 60 minutes (the second occurrence of the multiples of 10 and 15). The next occurrence after the 2nd clock would be 90 minutes.
Therefore, the bell and buzzer would be heard together next at 90 minutes.
To find the next time when both the bell and the buzzer would be heard, we need to find the least common multiple (LCM) of the time intervals, which are 10 minutes and 15 minutes.
Step 1: Calculate the LCM of 10 minutes and 15 minutes.
To find the LCM, we can list the multiples of each number until we find a common multiple.
Multiples of 10: 10, 20, 30, 40, 50, 60...
Multiples of 15: 15, 30, 45, 60...
The least common multiple of 10 and 15 is 30.
Step 2: Determine the starting point.
The bell and buzzer were last heard at the 2nd clock. So, we need to find the next multiple of 30 after the 2nd clock.
Multiples of 30: 30, 60, 90, 120, 150, 180...
The next multiple of 30 after the 2nd clock is the 30 itself.
Therefore, the bell and buzzer would both be heard next at 2:30 on the clock.