Question

The ratio of two numbers is 3 : 4 and their H.C.F is 4. Their L.C.M is

Answer 1

$\huge\text{\underline{Answer}}$

$\sf{\underline{Given }}$

The ratio of two number is 3 : 4.

H. C. F = 4

$\sf{\underline{To find }}$

L. C. M = ?

$\huge\sf{solution:}$

Let the number in ratio be 3x and 4x.

Now, The product of two numbers = product of its L. C. M and H. C. F

$\implies$ $\bold{3x × 4x = 4 × L. C. M }$

$\implies$ $\bold{L.C.M = \frac{12 {x}^{2} }{4} }$

$\implies$ $\bold{L.C.M = 3 {x}^{2} }$

But the L. C. M of 3x and 4x is 12x

$\implies$ $\bold{ 3 {x}^{2} = 12x}$

$\implies$ $\bold{3 x = 12 }$

$\implies$ $\bold{x = 4}$

Now L. C. M is $\bold{3 ×{4}^{2} }$

L. C. M = $\bold{48}$

Answer 2

Answer:

48

Step-by-step explanation:

x*y = LCM*HCF

3a*4a = LCM*4

LCM = 12$a^{2}$ / 4 = 3$a^{2}$

=> 3a*4a = 3$a^{2}$

=> 12a = 3$a^{2}$

=> a = 4

=> 3$a^{2}$

=> 3($4^{2}$)

=> 3*16

=> 48