Amit wants to organize his marbles by putting them in bags. If he places 3 marbles in each bag, he has 2 left. If he places 4 marbles in each bag, he has2 left. If he places 5 marbles in each bag, he has 2 left. What is the minimum number of marbles Amit has??
Answers
Given : Amit wants to organize his marbles by putting them in bags.
If he places 3 marbles in each bag, he has 2 left.
If he places 4 marbles in each bag, he has2 left.
If he places 5 marbles in each bag, he has 2 left.
To Find : What is the minimum number of marbles Amit has
Solution:
Marbles = M
M = 3A + 2 => M - 2 = 3A
M = 4B + 2 => M - 2 = 4B
M = 5C + 2 => M -2 = 5C
Hence M - 2 is LCM of 3 , 4 * 5
LCM of 3 , 4 and 5 = 60
M - 2 = 60
=> M = 62
minimum number of marbles Amit has 62
62 = 3 x 20 + 2
62 = 4 x 15 + 2
62 = 5 x 12 + 2
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