61 pennies
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We are looking for an LCM that results in a remainder of 1 when the bag of pennies is divided by 4, 5, or 6.
Applying this to the numbers 4, 5, and 6, the least common multiple is 60. This means that when we distribute 60 pennies into groups of 4, 5, or 6, there will be no remainders, as 60 is perfectly divisible by these numbers.
However, to fit our condition of having one penny left when dividing by these numbers, we need to add one to the LCM.
The result is 61 pennies.
So, the smallest possible number of pennies the bag could contain, given that there's one penny left when they're divided into equal groups of 4, 5 or 6, is 61 pennies.