Question
Find the least 4-digit number which, when divided by
16, 20, and 25, leaves a remainder of 7 in each case.Solution
Prime factorization of 16 = 2⁴
Prime factorization of 20 = 2² × 5
Prime factorization of 25 = 5² LCM of (16, 20, and 25) = 2⁴ × 5² = 16 × 25 = 400 Least 4-digit number divisible by 400 = 1,200 So, required number = 1200 + 7 = 1,207 Hence, option B.
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