model 5 lcm & hcf vs ratios Practice Questions Answers Test with Solutions & More Shortcuts
LCM & HCF PRACTICE TEST [5 - EXERCISES]
model 1 Basic formula of LCM & HCF
model 2 find lcm of numbers
model 3 find hcf of numbers
model 4 addition, subtraction, multiplication and division with lcm & hcf
model 5 lcm & hcf vs ratios
Question : 6 [SSC CGL 2010]
Two numbers are in the ratio 3 : 4. Their L.C.M. is 84. The greater number is
a) 28
b) 21
c) 24
d) 84
Answer »Answer: (a)
Let the numbers be 3x and 4x.
∴ Their LCM = 12x
∴ 12x = 84
⇒ x = $84/12$ = 7
∴ Larger number = 4x = 4 × 7 = 28
Question : 7 [SSC DEO 2009]
Two numbers are in the ratio 3 : 4. The product of their H.C.F. and L.C.M. is 2028. The sum of the numbers is
a) 86
b) 68
c) 72
d) 91
Answer »Answer: (d)
Using Rule 1,
1st number × 2nd number = L.C.M. × H.C.F
Let the numbers be 3x and 4x respectively
First number × second number
= HCF × LCM
⇒ 3x × 4x = 2028
⇒ $x^2 = 2028/{3×4}$ = 169
∴ x = $√{169}$ = 13
∴ Sum of the numbers
= 3x + 4x = 7x = 7 × 13 = 91
Question : 8
If the ratio of two numbers is 2 : 3 and their L.C.M. is 54, then the sum of the two numbers is
a) 45
b) 5
c) 15
d) 270
Answer »Answer: (a)
Let the two numbers are 2x and 3x respectively.
According to question,
LCM = 54
x (3×2)= 54
⇒ x = 9
Numbers = 2x = 2 × 9 = 18
and, 3x = 3 × 9 = 27
Sum of the two numbers
= 18 + 27 = 45
Question : 9 [SSC CGL 2011]
The ratio of the sum to the LCM of two natural numbers is 7 : 12. If their HCF is 4, then the smaller number is :
a) 12
b) 20
c) 16
d) 8
Answer »Answer: (a)
Let the numbers be 4x and 4y
where x and y are prime to each other.
LCM = 4xy
∴ $(\text"4x+4y")/ \text"4xy"$ = $7/12$
⇒ 12 (x + y) = 7 xy
⇒ x = 3, y = 4
∴ Smaller number = 4 × 3 = 12
Question : 10 [SSC MTS 2013]
Two numbers are in the ratio 3 : 4. If their HCF is 4, then their LCM is
a) 36
b) 48
c) 42
d) 24
Answer »Answer: (b)
Numbers = 3x and 4x
HCF = x = 4
∴ LCM = 12x = 12 × 4 = 48
IMPORTANT quantitative aptitude EXERCISES
model 5 lcm & hcf vs ratios Shortcuts »
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Click to Start..LCM & HCF Shortcuts and Techniques with Examples
-
model 1 Basic formula of LCM & HCF
Defination & Shortcuts … -
model 2 find lcm of numbers
Defination & Shortcuts … -
model 3 find hcf of numbers
Defination & Shortcuts … -
model 4 addition, subtraction, multiplication and division with lcm & hcf
Defination & Shortcuts … -
model 5 lcm & hcf vs ratios
Defination & Shortcuts …
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