Question

At a math team meeting, the coach wants to give pieces of candy to
each student. The coach knows that there will be 9, 10, 11, or 12
students at the meeting. What is the smallest positive number of
pieces of candy that the coach should take to the meeting to be
certain that each student receives the same number of pieces of
candy and no candy is left over?

Answer 1

Answer:

1 is answer because 1 is smallest positive number there

Answer 2

The answer is 1980 candies.

GIVEN

At a math team meeting, the coach wants to give pieces of candy to each student. The coach knows that there will be 9, 10, 11, or 12 students at the meeting.

TO FIND

the smallest positive number of pieces of candy that the coach should take to the meeting to be certain that each student receives the same number of pieces of candy and no candy is left over?

SOLUTION

The above problem can be simply solved as follows;

Possible number of students at the meetings = 9,10,11 or 12

The smallest positive number of candy taken by the coach = LCM of 9,10, 11 and 12

LCM =

|9,10,11,12

2|9, 5, 11, 6

2|9,5,11,3

3|3,5,11,1

3|1,5,11,1

5|1,1,11,1

11|1, 1, 1, 1

LCM = 2 × 2 × 3 × 3 × 5 × 11

= 1980

Hence, The answer is 1980 candies.

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