Question

LCM of two numbers is double than the greater number . And the difference between smaller number and GCF is 4 . Then the smallest number is ____.

1) 8. 2)6. 3)12. 4)16. ​

Answer 1

Answer:

Step-by-step explanation:Let the numbers be x and y

Let x>y

LCM is double the greater number as per condition

Therefore LCM =2x

Gcf= y-4

We know that

LCM*HCF=x*y

Therefore,

2x*y-4=xy

2x*y-4-xy=0

Take x common

Therefore

X[2*(y-4)-y]=0

Since x cannot be zero

2y-8-y=0

Therefore

Y= 8

Answer 2

Given :  LCM of two numbers is double than the greater number . And the difference between smaller number and GCF is 4  

To find : the smaller number is ____.

Solution:

Let say smaller  number  =  a  

& larger number = b  

Then GCF = a   - 4    

HCF = 2b

Number 1 * number 2 = LCM * HCF

a * b  = (a - 4) 2b

=> a  = (a - 4) 2

=> a = 2a - 8

=> a = 8

Smaller number is 8

Another way  GCF = k

smaller number  = k + 4    larger number = ka  

(k + 4)ka =  k * 2ka

=> k + 4 = 2k

=> k = 4

k + 4 = 4 + 4 = 8

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