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.