Question

LCM of two numbers is 72 times HCF, the sum of the other LCM HCF is 584 If one of the number is 72 then the other number is with solution ​

Answer 1

LCM = 72 HCF 

LCM + HCF =584 

72*HCF + HCF =584 

73 *HCF =584 

HCF = 584/73=8 

Then, 

LCM = 72 *8 = 576 

Now, use the formula, 

1st number * second Number = LCM * HCF 

72 * (60+x)=576*8

4320+72x=4608

x=4 

Answer 2

The other number = 64

Given :

• LCM of two numbers is 72 times HCF

• The sum of the the LCM , HCF is 584

• One of the number is 72

To find :

The other number

Concept :

HCF :

For the given two or more numbers HCF is the greatest number that divides each of the numbers

LCM :

For the given two or more numbers LCM is the least number which is exactly divisible by each of the given numbers

Relation between HCF and LCM :

HCF × LCM = Product of the numbers

Solution :

Step 1 of 2 :

Calculate LCM , HCF

Here it is given that LCM of two numbers is 72 times HCF

∴ LCM = 72 × HCF - - - - - (1)

Again sum of the the LCM , HCF is 584

LCM + HCF = 584

⇒ 72 × HCF + HCF = 584 [ Using Equation 1 ]

⇒ 73 × HCF = 584

⇒ HCF = 584/73

⇒ HCF = 8

∴ LCM

= 72 × HCF

= 72 × 8

= 576

Step 2 of 2 :

Find the other number

HCF × LCM = Product of the numbers

$\displaystyle \sf{ \implies 8 \times 576 = 72 \times Other \: number }$

$\displaystyle \sf{ \implies Other \: number = \frac{8 \times 576}{72} }$

$\displaystyle \sf{ \implies Other \: number = 8 \times 8 }$

$\displaystyle \sf{ \implies Other \: number = 64 }$

Hence other number = 64

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