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) 544
(b) 540
(c) 454
(d) 450
The correct answers to the above question in:
Answer: (a)
Using Rule 4,
When a number is divided by a, b or c leaving same remainder ‘r’ in each case then that number must be k + r where k is LCM of a, b and c.
LCM of 15, 12, 20, 54 = 540
Then number = 540 + 4 = 544 [4 being remainder]
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Read more find lcm using formula Based Quantitative Aptitude Questions and Answers
Question : 1
Four runners started running simultaneously from a point on a circular track. They took 200 seconds, 300 seconds, 360 seconds and 450 seconds to complete one round. After how much time do they meet at the starting point for the first time ?
a) 4800 seconds
b) 2400 seconds
c) 3600 seconds
d) 1800 seconds
Answer »Answer: (d)
Required time = LCM of 200, 300, 360 and 450 seconds
= 1800 seconds
Question : 2
Find the largest number of four digits such that on dividing by 15, 18, 21 and 24 the remainders are 11, 14, 17 and 20 respectively.
a) 7664
b) 5675
c) 7556
d) 6557
Answer »Answer: (c)
15 = 3 × 5
18 = $3^2$ × 2
21 = 3 × 7
24 = $2^3$ × 3
LCM = 8 × 9 × 5 × 7 = 2520
The largest number of four digits = 9999
3$2439/2520$ = 9999
Required number = 9999 – 2439 – 4 = 7556
(Because 15 - 11 = 4
18 - 14 = 4
21 – 17 = 4
24 – 20 = 4)
Question : 3
What is the smallest number which leaves remainder 3 when divided by any of the numbers 5, 6 or 8 but leaves no remainder when it is divided by 9 ?
a) 243
b) 723
c) 603
d) 123
Answer »Answer: (a)
We find LCM of 5, 6 and 8
5=5
6=3×2
8=$2^3$
= $2^3$ ×3 × 5 = 8 × 15 = 120
Required number = 120K + 3
∴ when K = 2, 120 × 2 + 3 = 243 required no.
It is completely divisible by 9
Question : 4
The greatest number of four digits which when divided by 12, 16 and 24 leave remainders 2, 6 and 14 respectively is
a) 9998
b) 9807
c) 9970
d) 9974
Answer »Answer: (d)
Using Rule 5,
When a number is divided by P, Q or R leaving remainders X, Y or Z respectively such that the difference between divisor and remainder in each case is the same i
.e., (P – X) = (Q – Y) = (R – Z) = T
(say) then that (least) number must be in the form of (K – T),
Where K is LCM of P, Q and R
Here,12 – 2 = 10; 16 – 6 = 10; 24 – 14 = 10
Now, LCM of 12, 16 and 24 = 48
∴ The greatest 4–digit number exactly divisible by 48 = 9984
∴ Required number = 9984 – 10 = 9974
Question : 5
Three bells ring at intervals of 36 seconds, 40 seconds and 48 seconds respectively. They start ringing together at a particular time. They will ring together after every
a) 24 minutes
b) 18 minutes
c) 12 minutes
d) 6 minutes
Answer »Answer: (c)
Required answer = LCM of 36, 40 and 48 seconds
= 720 seconds
= $(720/60)$minutes = 12 minutes
Illustration :
2 | 36, | 40, | 48 |
2 | 18, | 20, | 24 |
2 | 9, | 10, | 12 |
3 | 9, | 5, | 6 |
3, | 5, | 2 |
∴ LCM = 2 × 2 × 2 × 2 × 3 × 3 × 5 = 720
Question : 6
A, B, C start running at the same time and at the same point in the same direction in a circular stadium. A completes a round in 252 seconds, B in 308 seconds and C in 198 seconds. After what time will they meet again at the starting point ?
a) 46 minutes 12 seconds
b) 45 minutes
c) 42 minutes 36 seconds
d) 26 minutes 18 seconds
Answer »Answer: (a)
Required time = LCM of 252, 308 and 198 seconds
2 | 252, | 308, | 198 |
2 | 126, | 154, | 99 |
7 | 63, | 77, | 99 |
9 | 9, | 11, | 99, |
11 | 1, | 11, | 11 |
1, | 1, | 1 |
∴ LCM = 2 × 2 × 7 × 9 × 11 = 2772 seconds
= 46 minutes 12 seconds
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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