The H.C.F. and L.C.M. of two 2-digit numbers are 16 and 480 respectively. The numbers are :

Question

40,50
50.56
60,68
80,96

Solutons With Key Points

Answer- D

Given that,
L.C.M. of the two 2-digit numbers = 480
H.C.F. of the two 2-digit numbers = 16
Hence, the numbers can be expressed as 16p and 16q, where p and q are prime to each other.
As we know that ,
First number × second number = H.C.F. × L.C.M.
⇒ 16p × 16q = 16 × 480

pq = (16 x 480)/ (16 x 16)
The possible pairs of p and q, matching the condition pq = 30 are :- (3, 10), (5, 6), (1, 30), (2, 15)
Since the numbers are of 2-digits each of them.
Hence, we can take consideration a pair is (5, 6)
i.e. p = 5 and q = 6
∴ Numbers are : 16p = 16 × 5 = 80 and 16q = 16 × 6 = 96