A scientist receives signals from three quasars (distant sources of radio energy). The first quasar sends signals every 84 seconds, the second quasar every 42 seconds, and the three quasar 30 seconds.
The scientist wishes to divide each of the three time intervals into the largest possible equal-size parts so that these parts are equal for all three times intervals. What is the size of the parts?
If all three signals are received at the same moment, what is the shortest length of time from the moment before two of the signals will again be received at the same time?
To find the largest possible equal-sized parts for each time interval, we need to find the greatest common divisor (GCD) of the three time intervals. In this case, the GCD of 84, 42, and 30 is 6.
Therefore, the size of the equal-sized parts is 6 seconds.
To find the shortest length of time before two of the signals will again be received at the same time, we need to find the least common multiple (LCM) of the three time intervals. In this case, the LCM of 84, 42, and 30 is 420 seconds.
Therefore, the shortest length of time before two of the signals will again be received at the same time is 420 seconds.