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) 1100
(b) 900
(c) 975
(d) 800
The correct answers to the above question in:
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
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
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 : 2
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 : 3
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
Question : 4
The sum of two numbers is 36 and their H.C.F. is 4. How many pairs of such numbers are possible ?
a) 1
b) 3
c) 2
d) 4
Answer »Answer: (b)
HCF of two numbers = 4.
Hence, the numbers can be given by 4x and 4y
where x and y are co-prime.
Then, 4x + 4y = 36
4 (x + y) = 36
x + y = 9
Possible pairs satisfying this condition are : (1, 8), (4, 5), (2, 7)
Question : 5
The number between 4000 and 5000 that is divisible by each of 12, 18, 21 and 32 is
a) 4023
b) 4302
c) 4032
d) 4203
Answer »Answer: (c)
2 | 12, | 18, | 21, | 32 |
2 | 6, | 9, | 21, | 16 |
3 | 3, | 9, | 21, | 8 |
1, | 3, | 7, | 8 |
LCM = 2 × 2 × 3 × 3 × 7 × 8 = 2016
∴Required number = 2016 × 2 = 4032
Question : 6
The sum of two numbers is 216 and their HCF is 27. How many pairs of such numbers are there?
a) 1
b) 3
c) 2
d) 0
Answer »Answer: (c)
HCF of two numbers = 27
Let the numbers be 27x and 27y
where x and y are prime to each other.
According to the question,
27x + 27y = 216
27 (x + y) = 216
x + y = $216/27$ = 8
Possible pairs of x and y = (1, 7) and (3, 5)
Numbers =(27, 189) and (81, 135)
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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