I have often wondered about the value of memorising the 20 by 20 times table. I also read somewhere where knowing 25 by 25 times table would significantly boost mental calculation speed. This statement is only true if one encounters those types of calculations often?
I’d like to know what people here think and whether they have found that going beyond the 12 x 12 has been a significant advantage in mental calculation speed.
I recommend learning the following, in order of priority:
Only after that would I continue with things like up to 19 × 19. I know my calculation facts pretty well, and even I don’t know e.g. 16 × 23 from memory because there isn’t much extra utility in the tables up to 25 × 25.
Great, what do you find useful about the 15 times table and the up to 19 x 9? I assume the latter aids division.
15-times table: quite often I need to find 15% or add 50%, for example, which basically involve multiplications by 15. Multiplying by e.g. 14 or 17 is less common.
19 × 9 means you can break lots of 2-digit multiplications into two steps. E.g. 17 × 74 = 1190 + 68, using the 17-times table.
You could go further and also learn the 23-times table, 74-times table etc., but that’s diminishing returns and I have other hobbies 
These ones I’ve found genuinely helpful though, and I accidentally know some sporadic higher ones too like 23 × 7 = 161, 37 × 8 = 296
Thank you for the explanation, it helps to understand why people prioritise certain calculations over others. Your point about diminishing returns is poignant and the reason I asked the original question. Given limited time where are we best focusing our efforts to get maximum returns.