One set of traffic lights takes 75 seconds to complete its sequence.
Another set takes 120 seconds to complete its sequence.
Both sets turn green at precisely 2 pm.
How many seconds later do both sets next turn green at the same time?

Question

One set of traffic lights takes 75 seconds to complete its sequence.
    Another set takes 120 seconds to complete its sequence.
Both sets turn green at precisely 2 pm.
How many seconds later do both sets next turn green at the same time?

anonymous · Answer

Find the least common multiple of 75 and 120, you have how many seconds.

hoblos · Answer

600

anonymous · Answer

thank you! whats the easiest way to find the LCM?

anonymous · Answer

120 and 75 both divide into 600 equally. Therefore 600 seconds = 10 minutes. So 2:10pm.

anonymous · Answer

$$75=3\times 5^2$$
$$120=2^3\times 3\times 5$$
$$LCM=2^3\times 3\times 5^2$$

anonymous · Answer

Yeah I was going to say, prime factorisation is probably the best method. But after a while and lots of practice you tend to just "recognise" numbers and what they go into.

anonymous · Answer

yup - but prime factorisation is the 'sure fire' way

anonymous · Answer

do you always ignore the number with a lower power when using prime factorisation, to find out the LCM?

anonymous · Answer

Here's a couple of useful links on prime factorisation: http://www.helpwithfractions.com/least-common-multiple.html http://www.mathsisfun.com/prime-factorization.html First results from Google ;)

anonymous · Answer

haha, thank you so much! :P

anonymous · Answer

if you just want the answer quickly and you are on the computer try this http://www.wolframalpha.com/input/?i=lcm+%2875%2C120%29

anonymous · Answer

cool link! wish you could get that in exams though..