Find the greatest length which can be contained exactly in $10$ m $5$ dm $2$ cm $4$ mm and $12$ m $7$ dm $5$ cm $2$ mm.

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Solution

$10 m 5 d m 2 c m 4 m m = 10524 m m$
$12 m 7 d m 5 c m 2 m m = 12752 m m$
The greatest length required is G.C.F of $10524 a n d 12752$
Using Euclid algorithm
$12752 = 10524 \times 1 + 2228$
$10524 = 2228 \times 4 + 1612$
$2228 = 1612 \times 1 + 616$
$1612 = 616 \times 2 + 380$
$616 = 380 \times 1 + 236$
$380 = 236 \times 1 + 144$
$236 = 144 \times 1 + 92$
$144 = 92 \times 1 + 52$
$92 = 52 \times 1 + 40$
$52 = 40 \times 1 + 12$
$40 = 12 \times 3 + 4$
$12 = 4 \times 3 + 0$
Hence G.C.F $= 4 m m$

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