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) 3 : 2
(b) 6 : 1
(c) 2 : 3
(d) 7 : 2
The correct answers to the above question in:
Answer: (b)
L.C.M. of 28 and 42
| 2 | 28, | 42 |
| 2 | 14, | 21 |
| 7 | 7, | 21 |
| 1, | 3 |
= 2 × 2 × 7 × 3 = 84
H.C. F. of 28 and 42
∴ H.C. F = 14
Required ratio = $84/14$ = 6 : 1
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Read more finding with ratios Based Quantitative Aptitude Questions and Answers
Question : 1
The ratio of two numbers is 3 : 4 and their HCF is 5. Their LCM is :
a) 15
b) 10
c) 60
d) 12
Answer »Answer: (c)
If the numbers be 3x and 4x,
then
HCF = x = 5
∴ Numbers = 15 and 20
∴ LCM = 60
Question : 2
The H.C.F. and L.C.M. of two numbers are 21 and 84 respectively. If the ratio the two numbers is 1 : 4, then the larger of the two numbers is
a) 48
b) 12
c) 108
d) 84
Answer »Answer: (d)
HCF of numbers = 21
∴ Numbers = 21x and 21y
Where x and y are prime to each other.
Ratio of numbers = 1 : 4
∴ Larger number = 21 × 4 = 84
Question : 3
Three numbers are in the ratio 1 : 2 : 3 and their HCF is 12. The numbers are
a) 4, 8, 12
b) 12, 24, 36
c) 5, 10, 15
d) 10, 20, 30
Answer »Answer: (b)
Numbers = x , 2 x and 3 x (let)
Their H.C.F. = x = 12
∴ Numbers = 12, 24 and 36
Question : 4
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 : 5
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 : 6
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
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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