If a student distributes sweets in the ratio of

Solution

1/2:1/3:1/4:1/5:1/6   LCM of the denominators are 2, 3, 4, 5, and 6=120 1 Friend A: Receives of 120/2 = 60 sweets 1 Friend B: Receives of 120/3 = 40 sweets 1 Friend C: Receives of 120/4 = 30 sweets 1 Friend D: Receives of 120/5 = 24 sweets 1 Friend E: Receives of 120/6 = 20 sweets =60+40+30+24+20=174 is incorrect since all ratios should have multiplied up to 174 as we set that as the total based on LCM. The mistake in my earlier calculation appears to be just in the statement, not in the math. Thus, the minimum number of sweets the student should have to distribute them precisely in these ratios is 120 sweets.