In any army a proportion will not be front line troops but will be employed in logistics and other non-combat roles. If being optmistic we say for every Ivan in his tank there are two other soldiers in support then the direct combat numbers on his 150,000 will be 50,000. These will be spread over three fronts so perhaps it's not surprising that progress is slow. If Putin's intention to conquer and hold the whole country then he is going to have to deploy far more troops.
In terms of how many if we look at the invasion of Czechslovakia in 1968 the intial invasion force was 250,000 rising to 500,000 later. This for a smaller country than Ukraine and where the resistance was minimal.