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) 4800 seconds
(b) 2400 seconds
(c) 3600 seconds
(d) 1800 seconds
The correct answers to the above question in:
Answer: (d)
Required time = LCM of 200, 300, 360 and 450 seconds
= 1800 seconds
Discuss Form
Read more find lcm using formula Based Quantitative Aptitude Questions and Answers
Question : 1
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 : 2
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 : 3
The largest number of five digits which, when divided by 16, 24, 30, or 36 leaves the same remainder 10 in each case, is :
a) 99350
b) 99269
c) 99370
d) 99279
Answer »Answer: (c)
Using Rule 9,
The n digit largest number which when divided by a, b, c, leaves remainder ‘x’ will be
Required number = [n – digit largest number – R] + x
where, R is the remainder obtained when n – digit largest number is divided by the L.C.M of a, b, c.
We will find the LCM of 16, 24, 30 and 36
2 | 16, | 24, | 30, | 36 |
2 | 8, | 12, | 15, | 18 |
2 | 4, | 6, | 15, | 9 |
3 | 2, | 3, | 15, | 9 |
2, | 1, | 5, | 3 |
∴ LCM = 2 × 2 × 2 × 3 × 2 × 5 × 3 = 720
The largest number of five digits = 99999
On dividing 99999 by 720, the remainder = 639
∴ The largest five-digit number divisible by 720
= 99999 – 639 = 99360
∴ Required number = 99360 + 10
= 99370
Question : 4
The least number, which when divided by 12, 15, 20 or 54 leaves a remainder of 4 in each case, is :
a) 544
b) 540
c) 454
d) 450
Answer »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]
Question : 5
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 : 6
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
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 …
Verbal Reasoning
Question & Answer Quiz
Non Verbal Reasoning
Question & Answer Quiz
Quantitative Aptitude
Question & Answer Quiz
Computer MCQ
Question & Answer Quiz
General English
Question & Answer Quiz
History GK
Question & Answer Quiz
Polity GK
Question & Answer Quiz
Geography GK
Question & Answer Quiz
Economy GK
Question & Answer Quiz
General Awareness GK
Question & Answer Quiz
Recently Added Subject & Categories For All Competitive Exams
100+ Quadratic Equation Questions Answers PDF for Bank
Quadratic Equation multiple choice questions with detailed answers for IBPS RRB SO. more than 250 Attitude practice test exercises for all competitive exams
Continue Reading »
IBPS Aptitude Linear Equations MCQ Questions Answers PDF
Linear equations multiple choice questions with detailed answers for IBPS RRB SO. more than 250 Attitude practice test exercises for all competitive exams
Continue Reading »
New 100+ Compound Interest MCQ with Answers PDF for IBPS
Compound Interest verbal ability questions and answers solutions with PDF for IBPS RRB PO. Aptitude Objective MCQ Practice Exercises all competitive exams
Continue Reading »
100+ Mixture and Alligation MCQ Questions PDF for IBPS
Most importantly Mixture and Alligation multiple choice questions and answers with PDF for IBPS RRB PO. Aptitude MCQ Practice Exercises all Bank Exams
Continue Reading »