The text{g.c.d.} (greatest common divisor) of | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) We know that for any two positive integers $a$ and $b$,the relationship between their $	ext{g.c.d.}$ and $	ext{l.c.m.}$ is given by the formula:

Vedclass · Accepted Answer

$192$

Vedclass · Answer

(B) We know that for any two positive integers $a$ and $b$,the relationship between their $	ext{g.c.d.}$ and $	ext{l.c.m.}$ is given by the formula:$	ext{g.c.d.}(a, b) 	imes 	ext{l.c.m.}(a, b) = a 	imes b$Given that the $	ext{g.c.d.}$ is $16$ and the product of the two numbers $(a 	imes b)$ is $3072$,we can substitute these values into the formula:$16 	imes 	ext{l.c.m.} = 3072$To find the $	ext{l.c.m.}$,divide $3072$ by $16$:$	ext{l.c.m.} = \frac{3072}{16}$$	ext{l.c.m.} = 192$Therefore,the $	ext{l.c.m.}$ of the two numbers is $192$.

The $\text{g.c.d.}$ (greatest common divisor) of two numbers is $16$ and their product is $3072$. Find their $\text{l.c.m.}$ (least common multiple).

Similar Questions

The decimal expansion of the rational number $\frac{33}{2^{2} \cdot 5}$ will terminate after

If two positive integers $p$ and $q$ can be expressed as $p = a b^{2}$ and $q = a^{3} b$,where $a$ and $b$ are prime numbers,then $LCM(p, q)$ is:

$\sqrt{12}$ and ........ are like surds.

The decimal expansion of $\frac{43}{2^{4} \times 5^{3}}$ will terminate after .......... digits.

The numbers $525$ and $3000$ are both divisible by $3, 5, 15, 25,$ and $75$. What is $HCF(525, 3000)$? Justify your answer.

Vedclass Test Series

Exam Paper Generator

Online Exam Module