Why we use 150 mm size cube for compressive strength testing

Max size of aggregate to be used in concrete is 37.5 mm.
It's 4 times to the 37.5 mm.
37.5 x 4 = 150

Thus cube mould size is 150 mm
For 20 mm aggregate size concrete 100 mm cube mould size could be used.
 
Sir,
Very well explained,
have a query w.r.t cube strength result for M30 after 28 Days we are obtained M45 result and Mix design is 270 Kg of cement and 110 Kg of GGBS / Per Cum for M30, can we reduce the cement content by 15 Kg to limit the over stengnth of cubes.
Please suggest
U would optimize the mix but before optimizing i would say check standard deviation as well as COV if these values are inline u may go for optimization by
considering thumb rule that for 1 MPA required 5 OPC suppose if u will get 5 MPA more than required then 5*5=25 kg but for factor of safety u would go for 50% i.e. 25/2=12.5 kg