Multiple choice

Find the least number which when divided by 15,16 and 25 leaves 4 as a remainder but is completely divisible by 11 means leaves no remainder?

  1. 7007

  2. 6446

  3. 8404

  4. 5335

  5. 7004
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The number must be of the form LCM(15, 16, 25) * k + 4. LCM(15, 16, 25) = 1200. Testing multiples: 1200*1+4=1204 (not div by 11), 1200*2+4=2404 (not div by 11), 1200*7+4=8404. 8404 / 11 = 764, which is divisible by 11.

AI explanation

First, find the least common multiple of the divisors 15, 16, and 25, which equals 1200. Because the required number leaves a remainder of 4 in these cases, it must take the form 1200k + 4. Testing the multiple k = 7 gives the number 8404, and dividing 8404 by 11 results in a quotient of 764 with a remainder of 0, proving it is completely divisible by 11.

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