model 2 find lcm of numbers 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) 1.30 p.m.
(b) 1.15 p.m.
(c) 1 p.m.
(d) 2 p.m.
The correct answers to the above question in:
Answer: (c)
LCM of 20, 30 and 40 minutes = 120 minutes
Hence, the bells will toll together again after 2 hours i.e. at 1 p.m.
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Read more find lcm using formula Based Quantitative Aptitude Questions and Answers
Question : 1
The number nearest to 10000, which is exactly divisible by each of 3, 4, 5, 6, 7 and 8, is :
a) 10000
b) 9996
c) 10080
d) 9240
Answer »Answer: (c)
LCM of 3, 4, 5, 6, 7, 8 = 840
11$760/840$ = 10000
Since, the remainder 760 is more than half of the divisor 840.
∴ The nearest number
= 10000 + (840 – 760) = 10080
Question : 2
A number which when divided by 10 leaves a remainder of 9, when divided by 9 leaves a remainder of 8, and when divided by 8 leaves a remainder of 7, is :
a) 1359
b) 359
c) 539
d) 1539
Answer »Answer: (b)
Using Rule 5,
Here, Divisor – remainder = 1
e.g., 10 – 9 = 1, 9 – 8 = 1, 8 – 7 = 1
∴ Required number = (L.C.M. of 10, 9, 8) –1
= 360 – 1 = 359
Question : 3
The least multiple of 7, which leaves the remainder 4, when divided by any of 6, 9, 15 and 18, is
a) 364
b) 184
c) 94
d) 76
Answer »Answer: (a)
LCM of 6, 9, 15 and 18
| 2 | 6, | 9, | 15, | 18 |
| 3 | 3, | 9, | 15, | 9 |
| 3 | 1, | 3, | 5, | 3 |
| 1, | 1, | 5, | 1 |
∴ LCM = 2 × 3 × 3 × 5 = 90
∴ Required number = 90k + 4,
which must be a multiple of 7 for some value of k.
For k = 4,
Number = 90 × 4 + 4 = 364,
which is exactly divisible by 7.
Question : 4
The least number which when divided by 16, 18, 20 and 25 leaves 4 as remainder in each case but when divided by 7 leaves no remainder is
a) 18004
b) 18002
c) 18000
d) 17004
Answer »Answer: (a)
LCM of 16, 18, 20 and 25 = 3600
∴ Required number = 3600K + 4 which is exactly divisible by 7 for certain value of K.
When K = 5,
number = 3600 × 5 + 4
= 18004 which is exactly divisible by 7.
Question : 5
The LCM of four consecutive numbers is 60. The sum of the first two numbers is equal to the fourth number. What is the sum of four numbers?
a) 24
b) 21
c) 14
d) 17
Answer »Answer: (c)
| 2 | 60 |
| 2 | 30 |
| 3 | 15, |
| 5 |
∴ 60 = 2 × 2 × 3 × 5
i.e., Numbers = 2, 3, 4 and 5
∴ Required sum = 2 + 3 + 4 + 5 = 14
Question : 6
The number nearest to 43582 divisible by each of 25, 50 and 75 is :
a) 43550
b) 43600
c) 43650
d) 43500
Answer »Answer: (c)
LCM of 25, 50 and 75 = 150
On dividing 43582 by 150, remainder = 82
290$82/150$ = 43582
∴ Required number = 43582 + (150 – 82)
= 43650
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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