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Find the length of the plank that can be used to measure the lengths $4$ m $20$ cm and $5$ m $4$ cm exactly, in the least time.
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Sol. $4$ m $20$ cm $= 420$ cm and $5$ m $4$ cm $= 504$ cm (1/2 Mark)
Size of plank should be maximum, so we will find HCF $(420, 504)$
$420 = 2^2 \times 3 \times 5 \times 7$ and $504 = 2^3 \times 3^2 \times 7$ (1 Mark)
HCF $(420, 504) = 84$ (1/2 Mark)
$\therefore$ the required length of the plank is $84$ cm
Size of plank should be maximum, so we will find HCF $(420, 504)$
$420 = 2^2 \times 3 \times 5 \times 7$ and $504 = 2^3 \times 3^2 \times 7$ (1 Mark)
HCF $(420, 504) = 84$ (1/2 Mark)
$\therefore$ the required length of the plank is $84$ cm