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) 12
(b) 8
(c) 6
(d) 10
The correct answers to the above question in:
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
Practice LCM & HCF (model 4 addition, subtraction, multiplication and division with lcm & hcf) Online Quiz
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Read more with math operations Based Quantitative Aptitude Questions and Answers
Question : 1
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 : 2
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 : 3
If the HCF and LCM of two consecutive (positive) even numbers be 2 and 84 respectively, then the sum of the numbers is
a) 30
b) 14
c) 26
d) 34
Answer »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
Question : 4
Let x be the smallest number, which when added to 2000 makes the resulting number divisible by 12, 16, 18 and 21. The sum of the digits of x is
a) 7
b) 6
c) 5
d) 4
Answer »Answer: (a)
2 | 12, | 16, | 18, | 21 |
2 | 6, | 8, | 9, | 21 |
3 | 3, | 4, | 9, | 21 |
1, | 4, | 3, | 7 |
LCM = 2 × 2 × 3 × 4 × 3 × 7 = 1008
Multiple of 1008 = 2016
∴ Required number = 2016 – 2000 = 16 = x
∴ Sum of digits of x = 1 + 6 = 7
Question : 5
A number x is divisible by 7. When this number is divided by 8, 12 and 16. It leaves a remainder 3 in each case. The least value of x is:
a) 148
b) 150
c) 149
d) 147
Answer »Answer: (d)
LCM of 8, 12 and 16 = 48
∴ Required number
= 48a + 3 which is divisible by 7.
x = 48a + 3 = (7 × 6a) + (6a + 3) which is divisible by 7.
i.e. 6a + 3 is divisible by 7.
When a = 3, 6a + 3 = 18 + 3 = 21
which is divisible by 7.
∴ x = 48 × 3 + 3 = 144 + 3 = 147
Question : 6
The LCM of two numbers is 44 times of their HCF. The sum of the LCM and HCF is 1125. If one number is 25, then the other number is
a) 1100
b) 900
c) 975
d) 800
Answer »Answer: (a)
Using Rule 1,
If the HCF = H,
then LCM = 44 H
44 H + H = 1125
→ 45 H = 1125
∴ H = $1125/45$ = 25
LCM = 44 × 25 = 1100
Now, First number × Second number = LCM × HCF
→ 25 × Second number = 1100 × 25
∴ Second number = ${1100 × 25}/25$ = 1100
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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