Question

LCM and HCF of two numbers are 360 and 5. Find the number of such possible pairs.
Select one:
a. 12
O b. 36
OC. 24
d. 18​

Answer 1

Answer:

360 ×5 = a× b

so on prime fatorisation,

= 5×2×2×2×3×3

possible ordered pairs are 6

Answer 2

(D) is the correct option.

Given:

LCM = 360

HCF = 5

To find: the number of such possible pairs

Solution:

Let the required numbers be x and y

It is given that,

LCM(x,y) = 360

HCF(x,y) = 5

We know that,

xy = LCM(x,y) x HCF(x,y)

⇒ xy = 360 x 5

⇒ xy = 1800

Now,

enlisting the number of possible pairs, we have

1800 = 1 x 1800

= 2 x 900

= 3 x 600

= 4 x 450

= 5 x 360

= 6 x 300

= 8 x 225

= 9 x 200

= 10 x 180

= 12 x 150

= 15 x 120

= 18 x 100

= 20 x 90

= 24 x 75

= 25 x 72

= 30 x 60

= 36 x 50

= 40 x 45

⇒ Number of pairs = 18

∴ There are 18 possible pairs.

SPJ2