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The largest 3 digit number which when divided by 69 and 12 to give a remainder of 1 is 829.

What we want is one more than a common multiple of 69 and 12.

The common multiples of 69 and 12 are the multiples of their least common multiple:

69 = 3 x 23

12 = 2^2 x 3

→ lcm = 2^2 x 3 x 23 = 276

The largest multiple of 276 which is a 3 digit number:

999 ÷ 276 = 3 r 171 → largest 3 digit multiple of 276 is 3 × 276 = 828

→ the required number is 828 + 1 = 829.

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โˆ™ 2015-07-30 09:27:45
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Q: Which is the greatest number of 3 digit which when divided by 69 and 12 leave a remainder of 1?
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