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

#### LCM & HCF PRACTICE TEST [5 - EXERCISES]

Question : 1 [S.S.C. (CGL)2002]

The LCM of two numbers is 1920 and their HCF is 16. If one of the number is 128, find the other number.

a) 204

b) 240

c) 260

d) 320

Using Rule 1 :

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

We have,

First number × second number = LCM × HCF

∴ Second number = \${1920 × 16}/128\$ = 240

Question : 2 [S.S.C. (CPO) 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) 160

b) 150

c) 120

d) 140

Product of two numbers = HCF × LCM

1280 = 8 × LCM

160 = LCM

Question : 3 [S.S.C. (CHSL) 2010]

The HCF of two numbers is 15 and their LCM is 225. If one of the number is 75, then the other number is ?

a) 105

b) 90

c) 60

d) 45

First Number x Second Number = HCF x LCM

Then, 75 x Second Number = 15 x 225

Second Number \$latex = \${15 x 225}/75 = 45\$

Therefore, other number is 45.

Question : 4 [S.S.C. (CGL) 2011]

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

a) 0

b) 1

c) 2

d) 3

The HCF and LCM of two numbers are 12 and 924.

Let the numbers be 12p and 12q where p and q are prime to each other.

∴ LCM = 12pq

∴ 12pq = 924

⇒ pq = 77

∴ Possible pairs are (1 , 77) and (7 ,11)

Hence , required answer is 2.

Question : 5 [S.S.C. (CGL) 2011]

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

a) 8

b) 12

c) 24

d) 35

We know that:

LCM is the least common multiple of the given numbers whereas HCF is the highest common factor of those numbers.

Then, LCM is the multiplication of one common factor of the numbers and the other different factors of the numbers.

Write the LCM = 120 into factored form, that is

120 = 2 × 2 × 2 × 3 × 5

= 4(2 × 3 × 5)

⇒ 4 is the common factor of the numbers.

So, the HCF of three numbers is a multiple of 4.

Multiples of 4: 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, ...

Therefore, 35 is not the multiple of 4, then 35 cannot be their HCF.

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