Multiple choice

Find the least number which when divided by $12, 15, 20$ and $54$ gives the same remainder $7$ in each case?

  1. $365$
  2. $535$
  3. $547$
  4. $275$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Find LCM(12, 15, 20, 54). 12=2^2*3, 15=3*5, 20=2^2*5, 54=2*3^3. LCM = 2^2 * 3^3 * 5 = 4 * 27 * 5 = 540. The number is LCM + remainder = 540 + 7 = 547.

AI explanation

Let the unknown number be N. Subtract the common remainder 7 from N, making N - 7 perfectly divisible by 12, 15, 20 and 54. The least such number is the lowest common multiple of 12, 15, 20 and 54. The LCM is 540, so N - 7 = 540 and therefore N = 547.

Keep practicing — related questions