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

Question : 26

The HCF of two numbers is 16 and their LCM is 160. If one of the number is 32, then the other number is

a) 80

b) 48

c) 112

d) 96

Answer: (a)

Using Rule 1 :

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

We know that,

First number × Second number = LCM × HCF

⇒ Second number = ${16 × 160}/32$ = 80

Question : 27 [SSC Investigator 2010]

The HCF and LCM of two numbers are 18 and 378 respectively. If one of the number is 54, then the other number is

a) 144

b) 126

c) 238

d) 198

Answer: (b)

Using Rule 1 :

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

Second number =${HCF × LCM}/{First number} $

= ${18 ×378}/54$ = 126

Question : 28 [SSC CGL Prelim 2008]

The HCF and product of two numbers are 15 and 6300 respectively. The number of possible pairs of the numbers is

a) 3

b) 4

c) 1

d) 2

Answer: (d)

Let the number be 15x and 15y, where x and y are co –prime.

∴ 15x × 15y = 6300

⇒ xy = $6300/{15 ×15}$ = 28

So, two pairs are (7, 4) and (14, 2)

Question : 29 [SSC CGL Tier-1 2011]

The L.C.M. of three different numbers is 120. Which of the following cannot be their H.C.F.?

a) 12

b) 8

c) 35

d) 24

Answer: (c)

LCM = 2 × 2 × 2 × 3 × 5

Hence, HCF = 4, 8, 12 or 24

According to question

35 cannot be H.C.F. of 120.

Question : 30

The H.C.F. of two numbers is 8. Which one of the following can never be their L.C.M.?

a) 48

b) 24

c) 60

d) 56

Answer: (c)

HCF of two numbers is 8.

This means 8 is a factor common to both the numbers. LCM is common multiple for the two numbers, it is divisible by the two numbers. So, the required answer = 60

IMPORTANT quantitative aptitude EXERCISES

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