Question

Cows and Pigeons work together in an animal farm. The cows prepare the fields with their manure and pigeons sow seeds they collect from nearby fields. Cows take a break every $16$ minutes whereas pigeons take a break every $18$ minutes. After how many minutes of starting their day’s work together can they break together?

• A. $36$
• B. $288$
• C. $144$
• D. $72$

Answer 1

The correct option is C $144$

The cows and the pigeons start their day’s work together. Since, cows take a break every $16$ minutes, they take a breaks in minutes equivalent to the multiples of $16.$ Similarly, pigeons take a break in minutes equivalent to the multiples of $18.$ They can meet when the minutes elapsed is equal to the common multiples of both $16$ and $18.$ So, in order to find the time at which they meet for the first time, we find the LCM of the numbers $16$ and $18.$

Prime factorization of $16$ and $18:$
$16=2^4$
$18=3^2\times 2$
$\therefore LCM=3^2\times 2\times 2^3=144$
Thus, they can share a break after $144$ minutes of starting their respective works for the day.