Question

When the whole number P is divided by 18,24 and 30,the remainder is 3,What is the least value of P?

Answer 1

Answer:

Suppose, the number be n;

then, n≡3(mod18)

and n≡3(mod24)

⟹ (n−3) is a common multiple of 18 & 24

but the least common multiple of 18 & 24 is 72

consequently, (n−3) must be a multiple of 72 .

i.e. (n−3) may be one of 72,72×2,72×3,72×4,⋯ etc

so,the smallest possible (n−3) is 72

in other words, the smallest possible n is 72+3=75

Answer 2

Answer: 75 is ur answer Hope it helps you