When the whole number P is divided by 18,24 and 30,the remainder is 3,What is the least value of P? About the author Lydia
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 Reply
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: 75 is ur answer Hope it helps you