Question

There are three consecutive road crossings at which traffic lights change after every $48$ seconds, $72$ seconds and $108$ seconds respectively If the lights change simultaneously at \[8:20:00\] hours, then at what time will they change again simultaneously?

Answer 1

Hint: First we have to define what the terms we need to solve the problem are.
Since in the traffic lights, there are a total of three road crossings where there, and that comes with changes of every $48$ second and $72$ second and $108$second (first, second, and third lights) since we need to find the common terms from this given information so we need to know about LCM, which is the least common multiple that is the simplest method to find the smallest common numbers from the given two or more than two numbers.

Complete step-by-step solution:
Since LCM is all about the common multiple that number in which multiple of two or more than two (we cannot find LCM of a single number because that number itself is a single number of LCM).
Then which is also to find the least common factor or the multiple of any two or more integers or numbers.
Let the lights of that traffic change simultaneously after every interval of every $48$ second, $72$ and $108$second respectively.
Hence the LCM of $48,72,108$ is enough to find, which can be rewritten as $2 \times 2 \times 2 \times 3 \times 3 \times 3 \times 2 = 432$ (common multiple of ).
Hence the LCM is $432$ seconds and which can be converted into $7\min 12\sec $ thus the next required change will be happening in \[8:20:00 + 7\min 12\sec \Rightarrow 8:27:12\] (eight hours and twenty-seven minutes and twelve seconds) is the required answer to this problem.

Note: Let one minute can be written as sixty seconds, so use this formula to convert minutes into seconds in the above simplification, also there are two other properties like GCD and HCF; GCD is the greatest common divisor and HCF is the highest common factor.
HCF states that the largest number will factor each member of the group from the given number.
LCM is finding the common multiples first from two or more numbers, and then easily find which number is the least common multiples of the given numbers.