A lighthouse flashes its light every 12 minutes. Another lighthouse every 18 minutes. If the two lighthouses flash together at 12:00 noon,at what time will they next flash together?
Easy way: from a start at 0,
first lighthouse flashes at 12,24,36,48,60,72,84,... minutes
2nd lighthouse flashes at 18,36,....
so my "guess" would be at 12:36
(that was too easy)
rigorous math approach
12 = 2*2*3
18 = 2*3*3
LCM = 2*2*3*3 = 36
so time is 12:36
btw, a lighthouse that flashes only every 18 minutes would
be useless and downright dangerous to depend on.
Are you sure it wasn't seconds? The solution would then be
12:00:36
Bobo ampota
To find the time when the two lighthouses will next flash together, we need to find the least common multiple (LCM) of their flashing intervals.
The first lighthouse flashes every 12 minutes, and the second lighthouse flashes every 18 minutes. The LCM of 12 and 18 can be calculated as follows:
Prime factorization of 12: 2^2 * 3
Prime factorization of 18: 2 * 3^2
To find the LCM, take the highest exponent for each prime factor:
LCM = 2^2 * 3^2 = 4 * 9 = 36
So, the two lighthouses will next flash together every 36 minutes.
Since they flash together at 12:00 noon, we need to add 36 minutes to find the next time:
12:00 noon + 36 minutes = 12:36 PM
Therefore, the two lighthouses will next flash together at 12:36 PM.
To find out when the two lighthouses will next flash together, we need to determine the least common multiple (LCM) of the two flash intervals.
In this case, the first lighthouse flashes every 12 minutes, and the second lighthouse flashes every 18 minutes.
To find the LCM of 12 and 18, we can list the multiples of each number and find the first common multiple:
Multiples of 12: 12, 24, 36, 48, ...
Multiples of 18: 18, 36, 54, 72, ...
The first common multiple of 12 and 18 is 36, which means the two lighthouses will next flash together after 36 minutes from the initial flash at 12:00 noon.
To convert the 36-minute interval to hours and minutes, we divide 36 by 60 (since there are 60 minutes in an hour) to get:
36 ÷ 60 = 0.6 hours
Since there are 60 minutes in an hour, we multiply the decimal part (0.6) by 60 to convert it to minutes:
0.6 × 60 = 36 minutes
Therefore, the two lighthouses will next flash together 36 minutes after 12:00 noon, which is at 12:36 PM.