My sister has six children whose ages add up to 40. The ages of any two of her three boys have a common divisor greater than 1, and so do the ages of any two of the ages of her three girls. However, only one of the boy's ages has a common divisor with the age of one of the girls.

How old are my sister's six children?


They are

$3$, $3$, $6$, $7$, $7$, and $14$.

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