on a radio tower, a red light flashes every 6 seconds and a blue light flashes every 10 seconds. if both lights flash together at a certain time, how many seconds later will both lights flash together the next time
LCM(6,10) = 30
To find out when both lights will flash together again, we need to determine the least common multiple (LCM) of their time intervals. LCM is the smallest number that is divisible by both 6 and 10.
To find the LCM, we can list the multiples of each number and find the smallest common multiple:
Multiples of 6: 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, ...
Multiples of 10: 10, 20, 30, 40, 50, 60, ...
From the lists, we can see that the least common multiple of 6 and 10 is 30. Therefore, both lights will flash together again after 30 seconds.
In summary, the next time both lights will flash together will be 30 seconds later.