The number of students in a school is between 500 and 600. If we group them into groups of 12, 20, or 36 each, 7 students are always left over. How many students are in this school?
N mod 12 = 7
N mod 20 = 7
N mod 36 = 7
N = 547 - Number of students in the school.
547 was arrived at as follows:
The LCM[12, 20, 36] = 180, then smallest N is:
180m + 7 =187, where m=0, 1, 2, 3......etc.
Since the number of students is between 500 and 600 students, then:
180 * 3 + 7 = 547 - Number of students in this school.
