Need number that 3 5 and 8 go into?

The numbers which are divisible by 3, 5 & 8 are multiples of their LCM.

The lcm of 3, 5 & 8 is 3 x 5 x 8 = 120

So 3, 5 & 8 all divide into 120, 240, 360, 480, 600, ...