Find the smallest six-digit number exactly divisible by 111.

Given data & approach

• We want the least multiple of 111 that is ≥ 100000 (smallest six-digit number).

Step-by-step calculation

Compute the ceiling multiple: ⌈100000 / 111⌉111 × 900 = 99900111 × 901 = 100011 (≥ 100000)Thus the smallest six-digit multiple is 100011.

Verification

100011 ÷ 111 = 901 exactly; 100110 ÷ 111 = 902 with remainder −12; 100101 is not an exact multiple; 111000 is a multiple (×1000) but larger than 100011.

Common pitfalls

• Taking 111000 as the smallest just because it is a tidy multiple; it is not the least six-digit multiple.

Final Answer

100011