Question

The LCM of two numbers is 45 times their HCF.If one of the numbers is 125 and the sum of HCF and LCM is 1150.find out the other number?​

Answer 1

Solution :

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

The L.C.M of two numbers is 45 times their H.C.F. If one of the number is 125 & the sum of H.C.F & L.C.M is 1150.

$\underline{\bf{Explanation\::}}}}$

Let the other number be r

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

&

$\longrightarrow\sf{H.C.F + L.C.M = 1150}\\\\\longrightarrow\sf{H.C.F. + 45\:H.C.F = 1150\:\:[from(1)]}\\\\\longrightarrow\sf{46\:H.C.F=1150}\\\\\longrightarrow\sf{H.C.F=\cancel{1150/46}}\\\\\longrightarrow\bf{H.C.F=25}$

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

$\longrightarrow\sf{L.C.M=45\times 25}\\\\\longrightarrow\bf{L.C.M=1125}$

Now;

We know that formula :

$\boxed{\bf{Product\:of\:two\:number's =L.C.M\times H.C.F}}}$

$\longrightarrow\sf{125\times r=1125\times 25}\\\\\longrightarrow\sf{125r=28125}\\\\\longrightarrow\sf{r=\cancel{28125/125}}\\\\\longrightarrow\bf{r=225}$

Thus;

The other number will be 225 .

Answer 2

Your Answer:

We have given that

$\tt LCM(a,b) = 45 \times HCF(a,b)$

Here 'a' and 'b' are the numbers

And we have also

a = 125

And

HCF + LCM = 1150

Solution:-

Marking the Relation between LCM and HCF as Equations

$\tt \star LCM = 45 \times HCF \rightarrow \rightarrow \rightarrow \rightarrow(1) \\\\ \tt \star LCM + HCF = 1150 \rightarrow \rightarrow \rightarrow \rightarrow(2)$

Putting value of LCM from eq (1) in eq(2)

$\tt 45HCF + HCF = 1150 \\\\ \tt \Rightarrow 46HCF = 1150 \\\\ \tt \Rightarrow HCF = 25$

And

$\tt LCM = 45\times HCF \\\\ \tt \Rightarrow LCM = 45 \times 25 \\\\ \rr \Rightarrow 1125$

So,

We also know that

$\tt HCF \times LCM = a \times b \\\\ \tt \Rightarrow 25 \times 1125 = 125 \times b \\\\ \tt \Rightarrow b = \dfrac{25 \times 1125}{125} \\\\ \tt \Rightarrow b = 25 \times 9 \\\\ \tt \Rightarrow b = 225$

So, the another number is 225