model 4 addition, subtraction, multiplication and division with lcm & hcf 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) 30
(b) 14
(c) 26
(d) 34
The correct answers to the above question in:
Answer: (c)
Let the numbers be 2x and 2y
where x and y are prime to each other.
∴LCM = 2xy
⇒ 2xy = 84
⇒ xy = 42 = 6 × 7
∴ Numbers are 12 and 14.
Hence Sum = 12 + 14 = 26
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Read more with math operations Based Quantitative Aptitude Questions and Answers
Question : 1
The product of the LCM and HCF of two numbers is 24. The difference of the two numbers is 2. Find the numbers ?
a) 8 and 6
b) 2 and 4
c) 8 and 10
d) 6 and 4
Answer »Answer: (d)
Using Rule 1,
1st number × 2nd number = L.C.M. × H.C.F
Let the numbers be x and (x + 2).
∴ Product of numbers = HCF × LCM
⇒ x (x + 2) = 24
⇒ $x^2$ + 2x – 24 = 0
⇒ $x^2$ + 6x – 4x – 24 = 0
⇒ x (x + 6) – 4 (x + 6) = 0
⇒ (x – 4) (x + 6) = 0
⇒ x = 4, as x ≠ 6 = 0
∴ Numbers are 4 and 6.
Question : 2
The sum of two numbers is 45. Their difference is 1 9 of their sum. Their L.C.M. is
a) 200
b) 100
c) 250
d) 150
Answer »Answer: (b)
Let the number be x and y.
According to the question,
x + y = 45 ......... (i)
Again, x – y = $1/9$(x + y)
x – y = $1/9$×45
or x – y = 5 ..... (ii)
By (i) + (ii) we have,
x + y = 45
$\text"x – y = 5"/\text"2x"$ = 50
or, x = 25
y = 45 – 25 = 20.
Now, LCM of 25 and 20 = 100.
Question : 3
The L.C.M. of two numbers is 20 times their H.C.F. The sum of H.C.F. and L.C.M. is 2520. If one of the number is 480, the other number is :
a) 400
b) 520
c) 480
d) 600
Answer »Answer: (d)
Using Rule 1,
1st number × 2nd number = L.C.M. × H.C.F
Let the H.C.F. be H.
L.C.M. = 20H
Then, H + 20H = 2520
⇒ 21 H = 2520
⇒ H = $2520/21$ = 120
∴ L.C.M. = 20H = 20×120= 2400
As, First number × Second number = L.C.M. × H.C.F.
⇒ 480 × Second number = 2400 × 120
⇒ Second number = ${2400 × 120}/480$ = 600
Question : 4
The H.C.F. of two numbers, each having three digits , is 17 and their L.C.M. is 714. The sum of the numbers will be :
a) 289
b) 221
c) 391
d) 731
Answer »Answer: (b)
Let the numbers be 17x and 17y
where x and y are co-prime.
LCM of 17x and 17y = 17 xy
According to the question,
17xy = 714
⇒ xy = $714/17$ = 42 = 6 × 7
⇒ x = 6 and y = 7
or, x = 7 and y =6.
First number = 17x = 17 × 6 = 102
Second number = 17y =17 × 7 = 119
∴ Sum of the numbers = 102 + 119 = 221
Question : 5
Two numbers, both greater than 29, have HCF 29 and LCM 4147. The sum of the numbers is :
a) 966
b) 669
c) 696
d) 666
Answer »Answer: (c)
Let the number be 29x and 29y respectively
where x and y are prime to each other.
∴ LCM of 29x and 29y = 29xy
Now, 29xy = 4147
∴ xy = $4147/29$ = 143
Thus xy = 11 × 13
∴ Numbers are 29 × 11
= 319 and 29 × 13 = 377
∴ Required sum
= 377 + 319 = 696
Question : 6
The LCM of two positive integers is twice the larger number. The difference of the smaller number and the GCD of the two numbers is 4. The smaller number is :
a) 12
b) 8
c) 6
d) 10
Answer »Answer: (b)
Let the numbers be x H and yH
where H is the HCF and yH > x H.
LCM = xy H
xyH = 2yH
→ x = 2
Again, x H – H = 4
→ 2H – H = 4 ⇒ H = 4
∴ Smaller number = x H = 8
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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