Question

Aline has a number of sweets. She realises that if she shares the sweets equally among 3, 4, 5 or 6 friends, there will be no more sweets left. What is the least number of sweets she has?​

Answer 1

at least 60.

Explanation:

To solve this problem, we need to find the least common multiple (LCM) of 3, 4, 5, and 6, which is the smallest number that is divisible by all of them. To find the LCM, we first need to factor each number into its prime factors:

3 = 3

4 = 2 x 2

5 = 5

6 = 2 x 3

Then, we write down the prime factors with the highest exponent for each prime:

LCM = 2^2 x 3 x 5 = 60

This means that Aline has at least 60 sweets. To check, we can divide 60 by 3, 4, 5, and 6 to see if there is no remainder:

60 ÷ 3 = 20

60 ÷ 4 = 15

60 ÷ 5 = 12

60 ÷ 6 = 10

Therefore, Aline has at least 60 sweets, which she can share equally among 3, 4, 5, or 6 friends with no sweets left over.