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) xy z
(b) yz
(c) xz y
(d) xyz
The correct answers to the above question in:
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
Discuss Form
Read more finding with ratios Based Quantitative Aptitude Questions and Answers
Question : 1
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
Question : 2
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 : 3
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 : 4
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 »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 : 5
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 »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
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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