Two bells ring at hourly intervals of 5/7 and 7/8 respectively. The last time they rang together was at 4 am on Friday, at what time and which day will they ring together again?
I have tried to solve the question by taking the LCM of both the fractions by converting them to decimal but if I take the decimal value upto two places the answer is different than if I take the decimal value upto three places or one place.
The common denominator is $\operatorname{lcm}(7,8) = 56,$ so we observe that $$ \frac 5 7 = \frac{40}{56} \quad\text{and} \quad \frac 7 8 = \frac{49}{56}. $$ Then we have $\operatorname{lcm}(40,49) = 1960.$
Thus the next time they both ring simultaneously is $\dfrac{1960}{56}= 35.$