model 5 lcm & hcf vs ratios Section-Wise Topic Notes With Detailed Explanation And Example Questions
MOST IMPORTANT quantitative aptitude - 5 EXERCISES
The following question based on LCM & HCF topic of quantitative aptitude
(a) 86
(b) 68
(c) 72
(d) 91
The correct answers to the above question in:
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
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Read more finding with ratios Based Quantitative Aptitude Questions and Answers
Question : 1
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 : 2
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 : 3
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
Question : 4
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 : 5
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 »Answer: (a)
If the numbers be 2x and 3x,
then LCM = 6x
∴ 6x = 48 ⇒ x = 8
∴ Required sum = 2x + 3x = 5x
= 5 × 8 = 40
Question : 6
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 »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
LCM & HCF Shortcuts and Techniques with Examples
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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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