Model 5 Lcm & Hcf Vs Ratios Practice Questions Answers Test With Solutions & More Shortcuts

Question : 1 [SSC CPO S.I. 2003]

The ratio of two numbers is 4 : 5 and their L.C.M. is 120. The numbers are

a) 24, 30

b) 30, 40

c) 40, 32

d) 36, 20

Answer: (a)

Suppose the numbers are 4x and 5x respectively

According to question

x × 4 × 5 = 120

⇒ x = 6

∴ Required numbers

= 4 × 6 = 24

and = 5 × 6 = 30

Question : 2

Three numbers are in the ratio 2 : 3 : 4 and their H.C.F. is 12. The L.C.M. of the numbers is

a) 96

b) 144

c) 192

d) 72

Answer: (b)

Let the numbers be 2x, 3x and 4x respectively.

∴ HCF = x = 12

∴ Numbers are : 2 ×12 = 24

3 ×12 = 36, 4 ×12 = 48

LCM of 24, 36, 48

= 2 × 2 × 2 × 3 × 3 × 2 = 144

Question : 3 [SSC CHSL 2014]

If x : y be the ratio of two whole numbers and z be their HCF, then the LCM of those two numbers is

a) xy z

b) yz

c) xz y

d) xyz

Answer: (d)

Using Rule 1,

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

Product of two numbers

= HCF × LCM

⇒ Numbers = zx and zy

∴ zx × zy = z × LCM

⇒ LCM = xyz

Question : 4 [SSC CGL Prelim 2008]

Two numbers are in the ratio 3 : 4. If their LCM is 240, the smaller of the two number is

a) 60

b) 100

c) 80

d) 50

Answer: (a)

Let the number be 3x and 4x.

Their LCM = 12x

According to the question,

12x = 240

⇒ x = $240/12$ = 20

∴ Smaller number = 3x = 3 × 20 = 60

Question : 5 [SSC MTS 2011]

The LCM of two numbers is 48. The numbers are in the ratio 2 : 3. The sum of the numbers is

a) 40

b) 28

c) 32

d) 64

Answer: (a)

If the numbers be 2x and 3x,

then LCM = 6x

∴ 6x = 48 ⇒ x = 8

∴ Required sum = 2x + 3x = 5x

= 5 × 8 = 40

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