Question

the lcm of two numbers is 45 times their hcf. if one of the numbers is 225 and sum of their lcm and hcf is 1150, find the other number.

Answer 1

Let the HCF of the numbers be x.
⇒LCM of the numbers=45 times x=45*x=45x.
Sum of HCF and LCM is given as 1150 . 
Therefore , by the condition ,
45x+x=1150
⇒46x=1150
⇒x=1150/46=25.
⇒HCF of the numbers=25 and LCM of the numbers=25*45=1125.
Now we have the information
HCF=25 , LCM=1125 and one number=225.
We know the formula
(Product of HCF and LCM of 2 numbers)/(1 number)=Other number. Or,
25*1125/225
=5*1125/45
=1125/9
=125.
Ans:The numbers are 225 and 125.
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