Question

14. Two numbers are in the ratio 3 : 4. If their LCM is 180, find the numbers.
Hint. Let the required numbers be 3x and 4x.
Then, their LCM is 12x.
​

Answer 1

Given :-

• Two number are in ratio of 3 : 4
• LCM is 180

To find :-

• Numbers

Assume that :-

• 3 : 4 be in x form as 3x and 4x.
• H.C.F = x

Solution :-

● As we know that

${ \underline{ \boxed{ \bf{Product \: of \: two \: numbers = L.C.M × H.C.F}}}}$

So, according to the question value of x is

${ \implies{ \bf{3x \times 4x = 180 × x}}}$

${ \implies{ \bf{12 {x}^{2} = 180 x}}}$

${ \implies{ \bf{ \cfrac{12 {x}^{2}}{x} = 180 }}}$

${ \implies{ \bf{12 {x} = 180 }}}$

${ \implies{ \bf{ x= \cfrac{180}{12} }}}$

${ \large{ \underline{ \boxed{ \implies{ \bf{x = 15 }}}}}}$

■ So, numbers are :-

First number :

${ \large{ \bf{\implies{3 x}}}} \\ \\ \: \: \: \: \: \: \: \: \: \: { \large{ \bf{\implies{3 \times 15}}}} \\ \\{ \underline{ \boxed { \Large{ \red{ \bf{\implies{45}}}}}}}$

Second number :

${ \large{ \bf{\implies{4 x}}}} \\ \\ \: \: \: \: \: \: \: \: \: \: { \large{ \bf{\implies{4 \times 15}}}} \\ \\{ \underline{ \boxed { \Large{ \red{ \bf{\implies{60}}}}}}}$

● Final answer

• So, numbers are 45 and 60