LCM and HFC

Answer :

H.C.F. of the two digit numbers = 16
Hence, the numbers can be expressed as 16x and 16y,

where,
x and y are prime to each other.
Now,
First number × second number
= H.C.F. × L.C.M.
=> 16x × 16y = 16 × 480
=> xy = (16 x 480) / (16 x 16)
= 30
The possible pairs of x and y, satisfying the condition xy = 30 are :
(3, 10), (5, 6), (1, 30), (2, 15)

Since the numbers are of two digits each.
Hence, admissible pair is (5, 6)
Therefor Numbers are : 16 × 5 = 80
and 16 × 6 = 96

Answer :

We know that,
First number × Second number
= LCM × HCF
=> Second number = (16 x 160) / 32
= 80

Answer :

LCM = Product of two numbers / HCF
          = 4107 / 37
          = 111
Obviously, numbers are 111 and 37 which satisfy the given condition.
Hence, the greater number = 111

Answer :

First number × Second number
= HCF × LCM
Therefor Second number
= (15 x 300) / 60
= 75

Answer :

Let the numbers be 12x and 12y

where x and y are prime to each other.
therefore LCM = 12xy
therefore 12xy = 924
=> xy = 77
therefore Possible pairs = (1,77) and (7,11)