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) 10000
(b) 9996
(c) 10080
(d) 9240
The correct answers to the above question in:
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
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Read more find lcm using formula Based Quantitative Aptitude Questions and Answers
Question : 1
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 : 2
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 : 3
4 bells ring at intervals of 30 minutes, 1 hour, 1$1/2$ hour and 1 hour 45 minutes respectively. All the bells ring simultaneously at 12 noon. They will again ring simultaneously at :
a) 9 a.m.
b) 6 a.m.
c) 3 a.m.
d) 12 mid night
Answer »Answer: (a)
1$1/2$ hours = 90 minutes
1 hour and 45 minutes = 105 minutes
1 hour = 60 minutes
∴ LCM of 30 minutes, 60 minutes, 90 minutes and 105 minutes
3 | 30, | 60, | 90, | 105 |
5 | 10, | 20, | 30, | 35 |
2 | 2, | 4, | 6, | 7 |
1, | 2, | 3, | 7 |
∴ LCM = 3 × 5 × 2 × 2 × 3 × 7 = 1260 minutes
1260 minutes =$ 1260/60$ = 21 hours
∴ The bell will again ring simultaneously after 21 hours.
∴ Time will be
= 12 noon + 21 hours
= 9 a.m
Question : 4
Three bells ring simultaneously at 11a.m. They ring at regular intervals of 20 minutes, 30 minutes, 40 minutes respectively. The time when all the three ring together next is
a) 1.30 p.m.
b) 1.15 p.m.
c) 1 p.m.
d) 2 p.m.
Answer »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.
Question : 5
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 : 6
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
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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