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) 10224
(b) 10080
(c) 30256
(d) 50321
The correct answers to the above question in:
Answer: (b)
2 | 12, | 18, | 21 |
3 | 6, | 9, | 21 |
2, | 3, | 7 |
LCM of 12, 18 and 21
= 2 × 3 × 2 × 3 × 7 = 252
Of the options, 10080 ÷ 252 = 40
Practice LCM & HCF (model 4 addition, subtraction, multiplication and division with lcm & hcf) Online Quiz
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Question : 1
If A and B are the H.C.F. and L.C.M. respectively of two algebraic expressions x and y, and A + B = x + y, then the value of A3 + B3 is
a) x3 – y3
b) y3
c) x3
d) x3 + y3
Answer »Answer: (d)
Let no. are x and y and HCF = A, LCM = B
Using Rule, we have
xy = AB
⇒ x + y = A + B (given) ...(i)
$(x–y)^2$ = $(x+y)^2$ – 4xy
or, $(x–y)^2$ = $(A+B)^2$ – 4 AB
$(x–y)^2$ = $(A–B)^2$
(x–y) = A – B ...(ii)
Using (i) and (ii), we get
x = A and y = B
∴ $A^3 + B^3 = x^3 + y^3$
Question : 2
A number between 1000 and 2000 which when divided by 30, 36 and 80 gives a remainder 11 in each case is
a) 1451
b) 1712
c) 1641
d) 1523
Answer »Answer: (a)
We find LCM of 30, 36 and 80.
2 | 30, | 36, | 80 |
2 | 15, | 18, | 40 |
3 | 15, | 9, | 20 |
5 | 5, | 3, | 20 |
1, | 3, | 4 |
LCM = 2 × 2 × 3 × 3 × 4 × 5 = 720
∴ Required number = 2 × 720 + 11
= 1440 + 11 = 1451
Question : 3
The sum of a pair of positive integer is 336 and their H.C.F. is 21. The number of such possible pairs is
a) 2
b) 4
c) 3
d) 5
Answer »Answer: (b)
Let the numbers be 21x and 21y
where x and y are prime to each other.
21x + 21y = 336
21 (x + y) = 336
x + y = $336/21$ = 16
∴ Possible pairs = (1, 15), (5, 11), (7, 9), (3, 13)
Question : 4
The sum of the H.C.F. and L.C.M of two numbers is 680 and the L.C.M. is 84 times the H.C.F. If one of the number is 56, the other is :
a) 84
b) 8
c) 12
d) 96
Answer »Answer: (d)
Let HCF be h and LCM be l.
Then, l = 84h and l + h = 680
→ 84h + h = 680
→ h = $680/85$ = 8
∴ l = 680 – 8 = 672
∴ Other number = ${672× 8}/56$ = 96
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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