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The birthday of the grandson and grandfather

The birthday of the grandson and grandfather

A grandfather and his grandson turn years the same day. The circumstance is that for 6 consecutive years the age of the grandfather is a whole multiple of the age of the grandson.

What is the age of both in the sixth year that this coincidence occurs?

Solution

The grandfather will be 66 years old and the grandson 6 as:
66 = 6 * 11
65 = 5 * 13
64 = 4 * 16
63 = 3 * 21
62 = 2 * 31
61 = 1 * 61