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) 2
(b) 1
(c) –1
(d) –2
The correct answers to the above question in:
Answer: (d)
LCM of x and y = 161
∴ xy = 23 × 7
∴ x = 23; y = 7
∴ 3y – x = 3 × 7 – 23
= 21 – 23 = – 2
Discuss Form
Read more find lcm using formula Based Quantitative Aptitude Questions and Answers
Question : 1
Four bells ring at intervals of 4, 6, 8 and 14 seconds. They start ringing simultaneously at 12.00 O’clock. At what time will they again ring simultaneously ?
a) 12 hrs. 3 min. 44 sec.
b) 12 hrs. 3 min. 20 sec.
c) 12 hrs. 3 min.
d) 12 hrs. 2 min. 48 sec.
Answer »Answer: (d)
LCM of 4, 6, 8, 14
= 168 seconds
= 2 minutes 48 seconds
They ring again at 12 + 2 min. 48 sec.
= 12 hrs. 2 min. 48 sec.
Question : 2
Find the least number which when divided separately by 15, 20, 36 and 48 leaves 3 as remainder in each case.
a) 723
b) 483
c) 243
d) 183
Answer »Answer: (a)
Using Rule 4,
i.e. When a number is divided by x, y or z leaving same remainder ‘R’ in each case then that number must be K + R where k is LCM of x, y and z.
Required number = (LCM of 15, 20, 36 and 48) + 3
2 | 15, | 20, | 36, | 48 |
2 | 15, | 10, | 18, | 24 |
3 | 15, | 5, | 9, | 12 |
5 | 5, | 5, | 3, | 4 |
1, | 1, | 3, | 4 |
∴ LCM = 2 × 2 × 3 × 5 × 3 × 4 = 720
∴ Required number = 720 + 3 = 723
Question : 3
What is the least number which when divided by the numbers 3, 5, 6, 8, 10 and 12 leaves in each case a remainder 2 but when divided by 13 leaves no remainder ?
a) 1586
b) 1562
c) 962
d) 312
Answer »Answer: (c)
LCM of 3, 5, 6, 8, 10 and 12 = 120
∴ Required number = 120x + 2, which is exactly divisible by 13.
120x + 2 = 13 × 9x + 3x + 2
Clearly 3x + 2 should be divisible by 13.
For x=8,3x + 2 is divisible by 13.
∴ Required number = 120x + 2 = 120 × 8 + 2
= 960 + 2 = 962
Question : 4
Five bells begin to toll together and toll respectively at intervals of 6, 7, 8, 9 and 12 seconds. After how many seconds will they toll together again ?
a) 318 Sec.
b) 504 Sec.
c) 612 Sec.
d) 72 Sec.
Answer »Answer: (b)
Required time = LCM of 6, 7, 8, 9 and 12 seconds
= 504 seconds
Question : 5
The greatest number, which when subtracted from 5834, gives a number exactly divisible by each of 20, 28, 32 and 35, is
a) 5600
b) 5200
c) 4714
d) 1120
Answer »Answer: (c)
2 | 20, | 28, | 32, | 35 |
2 | 10, | 14, | 16, | 35 |
5 | 5, | 7, | 8, | 35 |
7 | 1, | 7, | 8, | 7 |
1, | 1, | 8, | 1 |
∴ LCM = 2 × 2 × 5 × 7 × 8 = 1120
∴ Required number
= 5834 – 1120 = 4714
Question : 6
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
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 »