If a student distributes sweets in the ratio of 

Solution

1/2:1/3:1/4:1/5:1/7   LCM of the denominators are 2, 3, 4, 5, and 7=420 1 Friend A: Receives of 420/2 = 210 sweets 1 Friend B: Receives of 420/3 = 140 sweets 1 Friend C: Receives of 420/4 = 105 sweets 1 Friend D: Receives of 420/5 = 84 sweets 1 Friend E: Receives of 420/7 = 60 sweets =210+140+105+84+60=599 is incorrect since all ratios should have multiplied up to 420 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 420 sweets.