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

Question : 36 [SSC CHSL 2014]

The H.C.F. and L.C.M. of two numbers are 44 and 264 respectively. If the first number is divided by 2, the quotient is 44. The other number is

a) 528

b) 147

c) 264

d) 132

Answer: (d)

Using Rule 1 :

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

First number = 2 × 44 = 88

∴ First number × Second number

= H.C.F. × L.C.M.

⇒ 88 × Second numebr

= 44 × 264

⇒ Second number = ${44 × 264}/88$ = 132

Question : 37 [SSC CHSL 2011]

The H.C.F. of two numbers is 96 and their L.C.M. is 1296. If one of the number is 864, the other is

a) 135

b) 132

c) 144

d) 140

Answer: (c)

Using Rule 1 :

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

First number × Second number = HCF × LCM

⇒ 864 × Second number

= 96 × 1296 ⇒ Second number

${96 × 1296}/864$ = 144

Question : 38 [SSC CGL Prelim 2002]

L.C.M. of two numbers is 1820 and their H.C.F. is 26. If one number is 130 then the other number is :

a) 1690

b) 70

c) 1264

d) 364

Answer: (d)

Using Rule 1 :

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

Given that

L.C.M. of two numbers = 1820

H.C.F. of those numbers = 26

One of the number is 130

∴ Another number = ${1820×26}/130$ = 364

Question : 39

The HCF of two numbers 12906 and 14818 is 478. Their LCM is

a) 200043

b) 400086

c) 800172

d) 600129

Answer: (b)

Using Rule 1 :

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

Product of two numbers = HCF × LCM

⇒ 12906 × 14818 = LCM × 478

⇒ LCM = ${12906 × 14818}/478$

= 400086

Question : 40

The LCM of two numbers is 30 and their HCF is 5. One of the number is 10. The other is

a) 25

b) 20

c) 5

d) 15

Answer: (d)

Using Rule 1 :

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

First number × second number = LCM × HCF

Let the second number be x.

∴ 10x = 30 × 5

>⇒ $x ={30 × 5}/10$ = 15

IMPORTANT quantitative aptitude EXERCISES

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