Question

State euclids division lemma and by using this find lcm and hcf where (a,b) =135,225

Answer 1

Euclid's decision lemma states that
Let
$\alpha \: and \: \beta$
be any two positive integers.
Then,there exists unique integers q and r such that
$\alpha = \beta q + r \: where \: 0 \leqslant r < \beta$
h.c.f of 135 and 225 is 45.
225=135×1 +90 (when r is not equal to 0)
135=90×1+45
90=45×2+0
thus 45 is h.c.f of 135,225