Problema Solution
Larissa has a bag of gumdrops. SHe knows there are fewer than 75 pieces of candy in all. When she divides them into groups of 3, 4, 5 or 6 there is always 1 gumdrop left over. How many gumdrops does Larissa have?
Answer provided by our tutors
We need to find The Least Common Multiple of 3, 4, 5 and 6 and add 1 (since there is always a reminder of 1):
LCM(3, 4, 5, 6) = 60 because
3 = 3^1
4 = 2^2
5 = 5^1
6 = 2*3
The LCM will be the product of multiplying the highest power of each prime number together:
LCM(3, 4, 5, 6) = = 3*(2^2)*5 = 60
60 + 1 = 61 and 61<= 75
Indeed:
3*20 + 1 = 61
4*15 + 1 = 61
5*12 + 1 = 61
6*10 + 1 = 61
Larissa has 61 gumdrops.