Question of the week 01-Feb-2018

The smallest value of 'M' for which 1 x 2 x 3 x ... x M is divisible by 888 is

a) 111              b) 44             c) 37                d) 74

Sorry for the little delay in posting the new question. Answer to the previous week question here. Next week question here. Current question is part of my upcoming book and it is solvable in less than 10 seconds. Your answer only with a logical explanation is welcomed in the comments section. Stay tuned for the technique and the answer. I am  making sure that my upcoming book is with many such beautiful problems. Reading it will provoke new thoughts and bring out the best in you.

Solution (12-Feb-18):

888 = 8 * 111 = 2*2*2*3*37.  So, for 888 to divide the numerator, we need to have at least all those prime numbers in the numerator. So, the value of M can be any multiple of 37. As the question is about smallest value, it should be 37.