Problema Solution

what is the smallest number which exactly divisible by 12 and 32 when 5 is added to it?

Answer provided by our tutors

Let 'x' be the number we are looking for then


x + 5 is divisible by 12 and 32 then we can write


x + 5 = 12k, k >0, k is integer => x > 12 - 5 = 7


x + 5 = 32t, t>0, t is integer => x > 32 - 5 = 27


12k - 5 = 32t - 5


12k = 32t


k/t = 8/3


The smallest k and t for which k/t = 8/3 are k = 8 and t = 3 therefore x = 12*8 - 5 = 32*3 - 5 = 91 the solution.