Question

the HCF and LCM of two no. is are 15 and 1350 respectively.One of the numbers lies between 130 and 140,find the numbers

Answer 1

The HCF and LCM of two numbers are 15 and 1350 respectively. 
One of the numbers lies between 130 and 140, 
The numbers are 135 and 15

15=3x5 so 3 and 5 are the only common factors 
1350 = 2 x 3^3 x 5^2, so one number must have 3^3 as a factor, and one must have 5^2. 
If the same number has both, it must be at least 27x25 = 675. The other can only have a 2,3 and 5, so it would be 30 at the greatest. 

Therefore one number must have 27 and 5 as factors, and the other must have 25 and 3. So they are multiples of 135 and 75. The last factor to account for is 2, and that must go with 75 in order for one of the numbers to be between 130 and 135. 

So the numbers are 135 and 150.