A set of marbles can be divided in equal shares among $2$, $3$, $4$, $5$, or $6$ children with no marbles left over. What is the least number of marbles that the set could have?

Question

Mathematics

Petersen

16 January, 13:11

A set of marbles can be divided in equal shares among $2$, $3$, $4$, $5$, or $6$ children with no marbles left over. What is the least number of marbles that the set could have?

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Answers (1)

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Clay Peck · Answer 1

60

Step-by-step explanation:

The least common multiple of 2, 3, 4, 5, and 6 is 3*4*5 = 60.

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2, 3, 5 are primes, there will be at least one factor of each of those in number you're looking for.

4 = 2², so there must be 2 factors of 2 in the number you're looking for.

6 = 2*3, so is already covered by the factors we have listed so far.

LCM = 2²*3*5 = 60

The least number divisible by numbers 2 through 6 is 60.