Teaser 2971: Six sisters on the ski lift

From The Sunday Times, 1st September 2019 [link]

The sum of the ages of six sisters known to me is 92. Though there is no single whole number greater than 1 that simultaneously divides the ages of any three of them, I did notice this morning, while they lined up for the ski lift, that the ages of any two of them standing one behind the other, had a common divisor greater than 1.

In increasing order, how old are the six sisters?

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