If text{g.c.d.} (a, b) = b,then text{l.c.m.} | vedclass

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Question

(B) We know the fundamental relationship between the greatest common divisor (g.c.d.) and the least common multiple (l.c.m.) of two positive integers

Vedclass · Accepted Answer

$a$

Vedclass · Answer

(B) We know the fundamental relationship between the greatest common divisor (g.c.d.) and the least common multiple (l.c.m.) of two positive integers $a$ and $b$ is given by the formula:$	ext{l.c.m.} (a, b) 	imes 	ext{g.c.d.} (a, b) = a 	imes b$Given that $	ext{g.c.d.} (a, b) = b$,we can substitute this into the formula:$	ext{l.c.m.} (a, b) 	imes b = a 	imes b$Dividing both sides by $b$ (since $b \in N$,$b 
eq 0$):$	ext{l.c.m.} (a, b) = \frac{a 	imes b}{b} = a$Therefore,the correct option is $B$.

If $\text{g.c.d.} (a, b) = b$,then $\text{l.c.m.} (a, b) = \dots$ (where,$a, b \in N$)

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