They are

6, 3 an 2

Because

36 = 3611 = 1821 = 1231 = 941 = 922 = 661 = 632 = 433

I assume every body is older than 1 (because the youngest can play piano)

$36 = 9*2*2 = 6*3*2 = 4*3*3 $
There is a youngest daughter (there can't be 2 youngest daughters) so they are 6, 3 and 2

But :

- You can be younger even if you have the same age
- I don't know any 2 years old girl who plays piano

##Answer no longer valid after edit

They are

6, 3 an 2

Because

36 = 3611 = 1821 = 1231 = 941 = 922 = 661 = 632 = 433

I assume every body is older than 1 (because the youngest can play piano)

$36 = 9*2*2 = 6*3*2 = 4*3*3 $
There is a youngest daughter (there can't be 2 youngest daughters) so they are 6, 3 and 2

But :

- You can be younger even if you have the same age
- I don't know any 2 years old girl who plays piano

They are

6, 3 an 2

Because

36 = 3611 = 1821 = 1231 = 941 = 922 = 661 = 632 = 433

I assume every body is older than 1 (because the youngest can play piano)

$36 = 9*2*2 = 6*3*2 = 4*3*3 $
There is a youngest daughter (there can't be 2 youngest daughters) so they are 6, 3 and 2

They are

6, 3 an 2

Because

36 = 3611 = 1821 = 1231 = 941 = 922 = 661 = 632 = 433

I assume every body is older than 1 (because the youngest can play piano)

$36 = 9*2*2 = 6*3*2 = 4*3*3 $
There is a youngest daughter (there can't be 2 youngest daughters) so they are 6, 3 and 2

But :

- You can be younger even if you have the same age
- I don't know any 2 years old girl who plays piano