What is the lowest number that is: (a) the sum of five consecutive numbers, and also (b) the sum of two consecutive odd numbers and also (c) the sum of three consecutive even numbers ?

30

4 + 5 + 6 + 7 + 8 = 30

14 + 16 = 30

8 + 10 + 12 = 30

Reference : Midgets Brain

It must be 60...

10-11-12-13-14 =60 five consecutive numbers

29-31 = 60 two consecutive odd numbers

18-20-22 = 60 three consecutive even numbers

To prove the smallest number that is the sum for all three cases:
a) the 5 consecutive numbers are n, n+1, n+2, n+3, n+4 where n is the first number; their sum is 5n+10, n=0,1,2,3,4,...; possible sums are 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, ...
b) the two consecutive odd numbers are m, m+2 where m is the smaller odd numbers; their sum is 2m+2, m=1,3,5,...; possible values are 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60, 64, ...
c) the three consecutive even numbers are x, x+2, x+4; their sum is 3x+6, x=0,2,4,6,...; possible values are 6, 15, 24, 33, 42, 51, 60, 69, ...

The first number that appears in all three lists is 60, so 60 is the lowest number that meets all three criteria.