Question

7) The LCM of two numbers is 14 times
their HCF . The sum of LCM and HCF is
600 if one number is 280, then find
the other number.​

Answer 1

Given,

• The LCM of two numbers is 14 times their HCF.
• The Sum of LCM and HCF is 600 , If one number is 280.

To Find,

• First Number = ?
• Other Number = ?

Solution :

$\longrightarrow$ Suppose the HCF of the Numbers be a

Therefore, The LCM of the Numbers be 14a

$\bigstar \huge{\underline{\orange{\tt{According\:to\:the\:Question :}}}}$

• The Sum of LCM and HCF is 600.

$\hookrightarrow \boxed{\sf{LCM + HCF = 600}}$

$\hookrightarrow \sf{14a + a = 600}$

$\hookrightarrow \sf{15a = 600}$

$\hookrightarrow \sf{a = \dfrac{600}{15}}$

$\hookrightarrow \boxed{\sf{a = 40}}$

Therefore,

• The HCF of Numbers = a = 40
• The LCM of Numbers = 14a = 14(40) = 560

$\bigstar \huge{\underline{\pink{\tt{Now,\:We\:Know\:that:}}}}$

$\longmapsto \boxed{\sf{LCM \times HCF = Product\:of\:Two\:Numbers}}$

$\longmapsto \sf{560 \times 40 = First\:Number \times Other\:Number}$

$\longmapsto \sf{22400 = 280 \times Other\:Number}$

$\longmapsto \sf{Other\:Number = \dfrac{22400}{280}}$

$\longmapsto \boxed{\red{\sf{Other\:Number = 80}}}$(Answer)

$\rule{200}2$

Answer 2

Step-by-step explanation:

✴️ Question ✴️

The LCM of two numbers is 14 times their HCF . The sum of LCM and HCF is 600 if one number is 280, then findthe other number.

✴️ANSWER ✴️

Let the other number be ′ x ′

Given:LCM+HCF=600

⇒14HCF+HCF=600

⇒15HCF=600

⇒HCF=40

⇒LCM=14×40=560

Since HCFxLCM=Product of 2 numbers

=>40×560 = 280×x

⇒x= 40×560/280

⇒x=40×2

⇒x=80

✴️So, other number is 80 ✴️