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) 9960
(b) 9930
(c) 9720
(d) 9690
The correct answers to the above question in:
Answer: (c)
Using Rule 8,
Greatest n digit number which when divided by three numbers A, B, C leaves no remainder will be
Required Number = (n – digit greatest number) – R
R is the remainder obtained on dividing greatest n digit number by L.C.M of A, B, C.
The largest number of 4-digits is 9999. L.C.M. of divisors
| 2 | 12, | 15, | 18, | 27 |
| 3 | 6, | 15, | 9, | 27 |
| 3 | 2, | 5, | 3, | 9 |
| 2, | 5, | 1, | 3 |
LCM = 2 × 2 × 3 × 3 × 3 × 5 = 540
Divide 9999 by 540, now we get 279 as remainder.
9999 – 279 = 9720
Hence, 9720 is the largest 4-digit number exactly divisible by each of 12, 15, 18 and 27.
Discuss Form
Read more find lcm using formula Based Quantitative Aptitude Questions and Answers
Question : 1
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
Question : 2
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 : 3
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 : 4
The least multiple of 13, which on dividing by 4, 5, 6, 7 and 8 leaves remainder 2 in each case is:
a) 840
b) 2522
c) 842
d) 2520
Answer »Answer: (b)
Using Rule 4,
LCM of 4, 5, 6, 7 and 8
=
| 2 | 4, | 5, | 6, | 7, | 8 |
| 2 | 2, | 5, | 3, | 7, | 4 |
| 1, | 5, | 3, | 7, | 2 |
= 2 × 2 × 2 × 3 × 5 × 7 = 840.
let required number be 840 K + 2 which is multiple of 13.
Least value of K for which (840 K + 2) is divisible by 13 is K = 3
∴ Required number
= 840 × 3 + 2
= 2520 + 2 = 2522
Question : 5
Which is the least number which when doubled will be exactly divisible by 12, 18, 21 and 30 ?
a) 196
b) 630
c) 1260
d) 2520
Answer »Answer: (b)
The LCM of 12, 18, 21, 30
| 2 | 12, | 18, | 21, | 30 |
| 3 | 6, | 9, | 21, | 15 |
| 2, | 3, | 7, | 5 |
∴LCM = 2 × 3 × 2 × 3 × 7 × 5 = 1260
∴ The required number
=$1260/2$ = 630
Question : 6
Three electronic devices make a beep after every 48 seconds, 72 seconds and 108 seconds respectively. They beeped together at 10 a.m. The time when they will next make a beep together at the earliest is
a) 10 : 07 : 48 hours
b) 10 : 07 : 36 hours
c) 10 : 07 : 24 hours
d) 10 : 07 : 12 hours
Answer »Answer: (d)
Required time = LCM of 48, 72 and 108 seconds
| 2 | 48, | 72, | 108 |
| 2 | 24, | 36, | 54 |
| 2 | 12, | 18, | 54 |
| 3 | 6, | 9, | 27 |
| 3 | 2, | 3, | 9 |
| 2, | 1, | 3 |
∴ LCM = 2 × 2 × 2 × 2 × 3 × 3 × 3 = 432 seconds
= 7 minutes 12 second
∴ Required time = 10 : 07 : 12 hours
LCM & HCF Shortcuts and Techniques with Examples
-
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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