Question

Two number 3:5 are in praportional, and the difference between 18 of these two number then what is the lcm

Answer 1

Let the two numbers be x and y where x>y

From the above data we can say

y/x=3/5

y=3x/5

We are also given that the difference of the two numbers is 18, hence

x-y=18

x-3x/5=18     (from above calculations)

2x/5=18

x=45

Since x=45 we can say that

45-y=18

y=27

we can express x and y as:

y=3*3*3

x=3*3*5

Therefore the LCM of x and y is the least common multiple which is

3*3*3*5=135

Hope this helps.

Answer 2

$\bf{\huge{\underline{\boxed{\sf{\red{Answer:}}}}}}$

$\bf{\large{\underline{\underline{\rm{\green{Given:}}}}}}$

• Two number 3:5 are in praportional
• The difference between the numbers 18

$\bf{\large{\underline{\underline{\rm{\green{To\:find:}}}}}}$

• LCM of the two numbers

$\bf{\large{\underline{\underline{\rm{\green{Solution:}}}}}}$

Let x be the common multiple of the of the ratio 3:5 .

•°• Greater number = 5x

Smaller number = 3x

$\bf{\large{\underline{\underline{\rm{\green{As\:per\:the\:question:}}}}}}$

• Difference between the numbers is 18

=> 5x - 3x = 18

=> 2x = 18

=> x = $\bf\large\frac{18}{2}$

=> x = 9

Substitute x = 9 in the values of the ratio,

$\bf{\large{\underline{\boxed{\sf{\orange{Greater\:number\:=\:5x\:=\:5\:\times\:9\:=45}}}}}}$

$\bf{\large{\underline{\boxed{\sf{\orange{Smaller\:number\:=\:3x\:=\:3\:\times\:9\:=27}}}}}}$

Now to find the LCM,

=> x = 45

$\begin{array}{r | l}</p><p></p><p>3 & 45 \\</p><p></p><p>\cline{2-2} 3 & 15 \\</p><p></p><p>\cline{2-2} 5 & 5 \\</p><p></p><p>\cline{2-2} & 1 \\</p><p></p><p>\end{array}$

x = 45 = 3 × 3 × 5

=> y = 27

$\begin{array}{r | l}</p><p></p><p>3 & 27 \\</p><p></p><p>\cline{2-2} 3 & 9 \\</p><p></p><p>\cline{2-2} 3 & 3 \\</p><p></p><p>\cline{2-2} & 1 \\</p><p></p><p>\end{array}$

=> y = 27 = 3 × 3 × 3

•°• LCM of 45 and 27 :-

=> 3 × 3 × 3 × 5

=> 9 × 3 × 5

=> 27 × 5

=> 135