a lighthouse flashes 3 seconds the second 4 and the third 5 seconds they flash initially al together when will they flash again together
What is the least common multiple of 3, 4, and 5?
60
60
To find the time when all the lighthouse flashes again together, you need to find the least common multiple (LCM) of the three flashing intervals: 3 seconds, 4 seconds, and 5 seconds.
First, let's list out the multiples of each interval:
Multiples of 3 seconds: 3, 6, 9, 12, ...
Multiples of 4 seconds: 4, 8, 12, 16, ...
Multiples of 5 seconds: 5, 10, 15, 20, ...
From the list, we notice that the number 12 appears as a multiple of all three intervals. Therefore, the lighthouse will flash again together after 12 seconds.
To calculate this more systematically, we can find the LCM by finding the prime factorization of each interval:
Prime factorization of 3 seconds: 3
Prime factorization of 4 seconds: 2^2
Prime factorization of 5 seconds: 5
Now, we take the highest power of each prime factor from the three factorizations:
Highest power of 2: 2^2 = 4
Highest power of 3: 3^1 = 3
Highest power of 5: 5^1 = 5
Finally, we multiply these highest powers together to get the LCM: 4 * 3 * 5 = 60 seconds.
Therefore, the lighthouse will flash again together after 60 seconds.