The least non-negative integer to be added to $64×65 × 66$ so that it is divisible by 67 is :
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 61
$64≡-3(mod\,67)$
$65≡-2(mod\,67)$
$66≡-1(mod\,67)$
$(-3)×(-2)×(-1)≡(-6)mod\,67$
$-6≡61(mod\,67)$
$⇒61+k≡0(mod\,67)$
$∴k=61$