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Euclid's Division Algorithm

M and N are...

Question

$M$ and $N$ are two natural numbers such that $M = 51$ . LCM of $M$ and $N$ is $255.$ What is/are the HCF of $M$ and $N ?$

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Solution

The correct options are
A $3$
D $1$
Product of two numbers is given by $H C F \times L C M$
$51 \times N = 255 \times H C F$
$N = 5 \times H C F$
LCM of $51, N = 255$
Hence $N = 5 K$
and K should be either 1 or 3 or 17
Hence $H C F = 1 o r 3 o r 17$

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