Question

LCM of 2 numbers is 45times their HCF. One of the number is 125 and sum of their HCF and LCM is 115a. Find the other number

Answer 1

Let the lcm be x and hcf be y and the other number be z.

Given lcm of 2 numbers is 45 times their hcf, the sum of HCF + LCM is 1150.

y = 45x. ---- (1)

x + y = 1150   --- (2)


Substitute equation (1) in (2), we get

46x = 1150

x = 25.


Substitute x = 25 in (1), we get

y = 45 * 25 = 1125.


We know that  product of two numbers = LCM * HCF

                                125 * z = 25 * 1125

                                z = 25 * 1125/125

                                   = 225.


The other number = 225.

Answer 2

AnswEr :

225.

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

LCM of two number is 45 times their HCF. One of the number is 125 and sum of their HCF and LCM is 1150.

$\bf{\red{\underline{\underline{\rm{To\:find\::}}}}}}$

The other number.

$\bf{\large{\blue{\underline{\underline{\tt{Explanation\::}}}}}}$

Let the other number be R

$\leadsto\sf{L.C.M\:=\:45\:\times H.C.F....................(1)}$

A/q

$\dashrightarrow\tt{L.C.M+H.C.F=1150}\\\\\\\dashrightarrow\tt{45\times H.C.F+H.C.F=1150\:\:\:\:\:\:\:\:\:\:\big[from(1)\big]}\\\\\\\dashrightarrow\tt{46\times H.C.F=1150}\\\\\\\dashrightarrow\tt{H.C.F=\cancel{\dfrac{1150}{46} }}\\\\\\\dashrightarrow\tt{\blue{H.C.F\:=\:25}}$

Putting the H.C.F in equation (1), we get;

$\dashrightarrow\tt{L.C.M\:=\:45\times 25}\\\\\\\dashrightarrow\tt{\blue{L.C.M\:=\:1125}}$

Now,

Formula use :

$\bf{\large{\boxed{\sf{Product\:of\:two\:numbers\:=\:L.C.M\:\times H.C.F}}}}}}$

$\longrightarrow\tt{125\times R\:=\:1125*25}\\\\\\\\\longrightarrow\tt{R\:=\:\dfrac{\cancel{1125} \times 25}{\cancel{125}} }\\\\\\\longrightarrow\tt{R\:=\:(9\times 25)}\\\\\\\longrightarrow\tt{\blue{R\:=\:225}}$

∴ The other number is 225.