model 1 Basic formula of LCM & HCF Practice Questions Answers Test with Solutions & More Shortcuts

Question : 31 [SSC CISF ASI 2010]

The product of two numbers is 216. If the HCF is 6, then their LCM is

a) 60

b) 72

c) 36

d) 48

Answer: (c)

Let the numbers be 6x and 6y where x and y are prime to each other.

∴ 6x × 6y = 216

⇒ xy = $216/{6 × 6}$ = 6

∴ LCM = 6xy = 6 × 6 = 36

Question : 32 [SSC CPO SI 2007]

The product of two numbers is 1280 and their H.C.F. is 8. The L.C.M. of the number will be :

a) 150

b) 160

c) 140

d) 120

Answer: (b)

Using Rule 1 :

1st number × 2nd number = L.C. M. × H.C.F,

HCF × LCM = Product of two numbers

⇒ 8 × LCM = 1280

⇒ LCM = $1280/8$ =160

Question : 33

The HCF and LCM of two numbers are 12 and 924 respectively. Then the number of such pairs is

a) 1

b) 0

c) 3

d) 2

Answer: (d)

Let the numbers be 12x and 12y where x and y are prime to each other.

∴ LCM = 12xy

∴ 12xy = 924

⇒ xy = 77

∴ Possible pairs = (1,77) and (7,11)

Question : 34 [SSC CGL Tier-I 2010]

The H.C.F. and L.C.M. of two numbers are 8 and 48 respectively. If one of the number is 24, then the other number is

a) 36

b) 48

c) 16

d) 24

Answer: (c)

Using Rule 1 :

1st number × 2nd number = L.C. M. × H.C.F,

First number × second number = HCF × LCM

⇒ 24 × second number = 8 × 48

∴ Second number =${8 × 48}/24$ = 16

Question : 35 [SSC CGL Prelim 1999]

LCM of two numbers is 225 and their HCF is 5. If one number is 25, the other number will be:

a) 25

b) 5

c) 225

d) 45

Answer: (d)

Using Rule 1 :

1st number × 2nd number = L.C. M. × H.C.F,

LCM × HCF = 1st Number× 2nd Number

⇒225 × 5 = 25 × x

∴ x = ${225 × 5}/25$ = 45

IMPORTANT quantitative aptitude EXERCISES

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