Find all pairs of natural numbers whose greatest common divisor is 5 and the least common multiple is 105.

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(1,525) , (3,175) , (7, 127), (56,12), (18,90), (525,1)

(1,525), (3,175), (21,25), (25,21), (175,3),(525,1), (280,14), (14,280), (9, 125), (125, 9)

(1,525), (3,175), (5,105), (15,35), (21,25), (25,21), (35,15), (105,5), (175,3), (525,1)

(525,1), (175,3), (210,2), (2,210), (3,175), (1,525), (5,97), (97,5), (45, 46), (45,45)

answer is C.

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Detailed Solution

Concept- Given, greatest common factor = 5,
Least common multiple = 105
Suppose, two numbers a and b, assume the product of both the numbers is Q,
Q = a×b
Suppose, greatest common divisor of a and b is P,
G.C.D. = P
Let least common multiple of a and b is Q,
L.C.M. = Q
Equating the equations,
a×b = P×Q
G.C.F. of two numbers is equal to 5, P = 5
L.C.M. of two numbers is equal to 105, Q = 105
a×b =5×105
a×b =525
Pairs are,
525×1=525
3×175=525
5×105=525
15×35=525
21×25=525
25×21=525
35×15=525
105×5=525
175×3=525
1×525=525
525,1, 3,175, 5,105, 15,35, 21,25, 25,21, 35,15, 105,5,175,3, 1,525
Hence, the correct option is 3) (1,525), (3,175), (5,105), (15,35), (21,25), (25,21), (35,15), (105,5), (175,3), (525,1).

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