Question

Find the smallest number that leaves 3 as a remainder when divided by 18 and 24

Answer 1

Answer:

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Answer 2

Step-by-step explanation:

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

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