Question

The two num lcm is the two number 5times more than hcf.Sum of lcm and hcf is 300.One number is 125 and another num

Answer 1

QUESTION :-

LCM of two numbers is 5 times more than HCF . Sum of LCM and HCF is 300 . If one of the number is 125 Then find the other Number

GIVEN :-

• LCM of two numbers is 5 times more than their HCF

• Sum of LCM and HCF is 300

• One of the number is 125

TO FIND :-

• Other Number

SOLUTION :-

We are given ,

$\underline {\bold {\boxed {\pink {\sf{LCM = 5HCF }}}}} \longrightarrow \sf equation(1)$

We have Sum of LCM and HCF as 300

$\implies \sf \: LCM + HCF = 300$

$\implies \sf 5HCF + HCF = 300 \\ \\ \implies \sf 6 HCF = 300 \\ \\ \implies \sf HCF = \frac{300}{6} \\ \\ \implies \sf HCF = \frac{ \cancel{300}}{ \cancel{6}} \\ \\ \implies {\underline {\bold {\boxed {\pink{\sf HCF = 50}}}}}$

From eq(1) ,

$\implies \sf LCM = 5HCF \\ \\ \implies \sf LCM = 5(50) \\ \\ \implies \underline{\bold {\boxed {\pink{\sf {LCM = 250}}}}}$

Now We have ,

• LCM = 250
• HCF = 50
• One of the number = 125

Let Other Number be ' x '

$\: \large {\underline {\bold {\boxed { {\sf{ \bigstar \:{ \red{ Product \: of \: two \: numbers = LCM \times HCF}}}}}}}}$

$\implies \sf \: 125 \times x = 250 \times 50 \\ \\ \implies \sf \: x = \frac{250 \times 50}{125} \\ \\ \implies \sf \:x = \frac{12500}{125} \\ \\ \implies \sf x = \frac{ \cancel{125}00 }{ \cancel{125}} \\ \\ \implies {\underline {\bold {\boxed {\blue{\sf { x= 100}}}}}}$

∴ The other Number is 100

Answer 2

Question :-

• The two num lcm is the two number 5times more than hcf.Sum of lcm and hcf is 300.One number is 125 and another num

Given :-

• LCM is the two number 5 times more than HCF.

• Sum of LCM and HCF is 300.

• One number is 125

To Find :-

• Another number

Solution :-

We are given ,

$\underline {\bold {\boxed {\green {\sf{LCM = 5HCF }}}}} \longrightarrow \sf equation(1) </p><p>$

We have Sum of LCM and HCF as 300

$\implies \sf \: LCM + HCF = 300$

$\implies \sf 5HCF + HCF = 300$

$\\ \implies \sf 6 HCF = 300$

$\\ \implies \sf HCF = \frac{300}{6}$

$\\ \implies \sf HCF = \frac{ \cancel{300}}{ \cancel{6}}$

$\\ \implies {\underline {\bold {\boxed {\green{\sf HCF = 50}}}}}$

$\underline{\bold{From \: eq \: (1)}}$

$\implies \sf LCM = 5HCF$

$\ \\ \implies \sf LCM = 5(50)$

$\\ \implies \underline{\bold {\boxed {\green{\sf {LCM = 250}}}}}$

$\underline{\bold{Now \: We \: have }}$

LCM = 250

HCF = 50

One of the number = 125

Let Other Number be ' x '

$\: \large {\underline {\bold {\boxed { {\sf{ \bigstar \:{ \red{ Product \: of \: two \: numbers = LCM \times HCF}}}}}}}} </p><p>$

$\implies \sf \: 125 \times x = 250 \times 50$

$\\ \implies \sf \: x = \frac{250 \times 50}{125}$

$\\ \implies \sf \:x = \frac{12500}{125}$

$\\ \implies \sf x = \frac{ \cancel{125}00 }{ \cancel{125}}$

$\\ \implies {\underline {\bold {\boxed {\pink{\sf { x= 100}}}}}}</p><p>$

${\bold{\bold{\boxed{∴ The \: other \: Number \: is \: 100}}}}$