Multiple choice

Find the greatest 5 digit number that will give us 15 as the remainder when divided by the LCM of 8 and 9.

  1. 99921

  2. 99951

  3. 99941

  4. 99851

  5. 99961
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B Correct answer
Explanation

The LCM of 8 and 9 is 72. The largest 5-digit number is 99999. Dividing 99999 by 72 gives 1388 with a remainder of 63. The largest multiple of 72 less than 99999 is 99999 - 63 = 99936. To get a remainder of 15, we add 15 to this multiple: 99936 + 15 = 99951.

AI explanation

The least common multiple of 8 and 9 is 72. For a number to leave a remainder of 15 when divided by 72, it must take the form 72k + 15. The greatest 5 digit number is 99999, and dividing it by 72 gives a quotient of 1388 and a remainder of 63. Therefore, subtracting (63 minus 15), which is 48, from 99999 gives 99951.

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