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) 1
(b) 3
(c) 2
(d) 4
The correct answers to the above question in:
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)
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
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
Question : 2
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 : 3
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 : 4
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 : 5
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)
Question : 6
The greatest four digit number which is exactly divisible by each one of the numbers 12, 18, 21 and 28 is
a) 9828
b) 9882
c) 9288
d) 9928
Answer »Answer: (a)
Using Rule 1,
1st number × 2nd number = L.C.M. × H.C.F
2 | 12, | 18, | 21, | 28 |
2 | 6, | 9, | 21, | 14 |
3 | 3, | 9, | 21, | 7 |
7 | 1, | 3, | 7, | 7 |
1, | 3, | 1, | 1 |
LCM = 2 × 2 × 3 × 3 × 7= 252
The largest 4-digit number = 9999
∴ Required number = 9999 – 171 = 9828
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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