# Real Number

Find the smallest natural number of the form 2 power a 3 power b 7 power c, such that half of the number is the cube of an integer,one third of the number is the seventh power of an integer, and one seventh of the number is the square of an integer.[Hint: 2^a3^b7^c/2 is a cube only if a-1,b,c are all divisible by 3.]