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) 196
(b) 630
(c) 1260
(d) 2520
The correct answers to the above question in:
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
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Read more find lcm using formula Based Quantitative Aptitude Questions and Answers
Question : 1
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 : 2
The largest 4-digit number exactly divisible by each of 12, 15, 18 and 27 is
a) 9960
b) 9930
c) 9720
d) 9690
Answer »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.
Question : 3
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 : 4
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
Question : 5
Find the greatest number of five digits which when divided by 3, 5, 8, 12 have 2 as remainder :
a) 99962
b) 99960
c) 99958
d) 99999
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.
The greatest number of five digits is 99999.
LCM of 3, 5, 8 and 12
2 | 3, | 5, | 8, | 12 |
2 | 3, | 5, | 4, | 6 |
3 | 3, | 5, | 2, | 3 |
1, | 5, | 2, | 1 |
∴ LCM = 2 × 2 × 3 × 5 × 2 = 120 After dividing 99999 by 120, we get 39 as remainder 99999 – 39 = 99960 = (833 × 120)
99960 is the greatest five digit number divisible by the given divisors.
In order to get 2 as remainder in each case we will simply add 2 to 99960.
∴ Greatest number = 99960 + 2 = 99962
Question : 6
The greatest number of four digits which when divided by 3, 5, 7, 9 leave remainders 1, 3, 5, 7 respectively is :
a) 9765
b) 9766
c) 9764
d) 9763
Answer »Answer: (d)
The difference between divisor and the corresponding remainder is equal.
LCM of 3, 5, 7 and 9 = 315 Largest 4-digit number = 9999
31$234/315$ = 9999
∴ Number divisible by 315 = 9999 – 234 = 9765
Required number = 9765 – 2 = 9763
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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