Smallest number of five digits is 10000. Required number must be divisible by L.C.M. of 16,24,36,54 i.e 432, On dividing 10000 by 432,we get 64 as remainder. Required number = 10000 +( 432 – 64 ) = 10368.
The number students in each room = HCF of 70,98 and 126 =14 In each room , maximum 14 students can be seated. Total number students = 70 + 98 +126 =294 Number of rooms required = 294/14 =21
Since the numbers are co-prime, they contain only 1 as the common factor.Also, the given two products have the middle number in common.So, middle number = H.C.F. of 551 and 1073 = 29;First number = 551/29 = 19; Third number = 1073/29 = 37.Required sum = (19 + 29 + 37) = 85.