Problema Solution
there are two numbers x and y such that x >y. their hcf is4 and lcm is 48.if 2 is added to y the hcf is increased by 2.if 2 is subtracted from x the hcf is reduced by 2. find values of x and y.
Answer provided by our tutors
hcf(x, y) = 4
lcf(x, y) = 48
using the fact that x*y = hcf(x, y)* lcf(x, y) we have
xy = 4*48
xy = 192
if 2 is added to y the hcf is increased by 2:
hcf(x, y+2) = 4 + 2
hcf(x, y+2) = 6 follows 6|x and since 4|x follows 3*4|x that is 12|x
if 2 is subtracted from x the hcf is reduced by 2
hcf(x-2, y) = 4 - 2
hcf(x-2, y) = 2
for x = 12 we have y = 192/12 that is y = 16
indeed
hcf(12, 16) = 4
lcf(12, 16) = 48
hcf(12, 16+2) = 6
hcf(12 - 2, 16) = 2