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 $B$.

Part $I$	Part $II$
$1. \text{l.c.m.}(8, 16, 24)$	$a. 36$
$2. \text{g.c.d.}(8, 16, 24)$	$b. 48$
$3. \text{l.c.m.}(6, 12, 18)$	$c. 8$
$4. \text{g.c.d.}(6, 12, 18)$	$d. 12$
	$e. 6$

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

Similar Questions

Which of the following groups correctly matches the data of Part $I$ with the data of Part $II$?

Part $I$ Part $II$

$1. \text{l.c.m.}(8, 16, 24)$ $a. 36$

$2. \text{g.c.d.}(8, 16, 24)$ $b. 48$

$3. \text{l.c.m.}(6, 12, 18)$ $c. 8$

$4. \text{g.c.d.}(6, 12, 18)$ $d. 12$

$e. 6$

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The least number that is divisible by all the numbers from $1$ to $10$ (both inclusive) is

The Least Common Multiple $(LCM)$ of the smallest prime number and the smallest composite number is . . . . . . .

Find the smallest integer that is divisible by both $28$ and $63$.

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