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) 3600
(b) 2500
(c) 1600
(d) 900
The correct answers to the above question in:
Answer: (a)
We find LCM of = 10, 16, 24
2 | 10, | 16, | 24 |
2 | 5, | 8, | 12 |
2 | 5, | 4, | 6 |
2 | 5, | 2, | 3 |
3 | 5, | 1, | 3 |
5 | 5, | 1, | 1 |
1, | 1, | 1 |
∴ LCM = $2^2$ × $2^2$ × 3 × 5
∴ Required number
= 2 × 2 × 2 × 2 × 3 × 3 × 5 × 5
= 3600
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Read more find lcm using formula Based Quantitative Aptitude Questions and Answers
Question : 1
When a number is divided by 15, 20 or 35, each time the remainder is 8. Then the smallest number is
a) 338
b) 328
c) 427
d) 428
Answer »Answer: (d)
Using Rule 5,
LCM of 15, 20 and 35 = 420
∴ Required least number = 420 + 8 = 428
Question : 2
If the students of a class can be grouped exactly into 6 or 8 or 10, then the minimum number of students in the class must be
a) 240
b) 180
c) 120
d) 60
Answer »Answer: (c)
Required number of students = LCM of 6, 8, 10 = 120
Question : 3
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
Question : 4
The least number which when divided by 4, 6, 8 and 9 leave zero remainder in each case and when divided by 13 leaves a remainder of 7 is :
a) 85
b) 36
c) 72
d) 144
Answer »Answer: (c)
LCM of 4, 6, 8, 9
2 | 4, | 6, | 8, | 9 |
2 | 2, | 3, | 4, | 9 |
3 | 1, | 1, | 2, | 3 |
1, | 1, | 2, | 3 |
∴ LCM = 2 × 2 × 3 × 2 × 3 = 72
∴ Required number = 72, because it is exactly divisible by 4, 6, 8 and 9 and it leaves remainder 7 when divided by 13.
Question : 5
Let the least number of six digits which when divided by 4, 6, 10, 15 leaves in each case same remainder 2 be N. The sum of digits in N is :
a) 6
b) 4
c) 5
d) 3
Answer »Answer: (c)
LCM of 4, 6, 10, 15 = 60
Least number of 6 digits = 100000
The least number of 6 digits which is exactly divisible by 60 = 100000 + (60 – 40) = 100020
∴ Required number (N) = 100020 + 2 = 100022
Hence, the sum of digits = 1 + 0 + 0 + 0 + 2 + 2 = 5
Question : 6
The least number, which when divided by 4, 5 and 6 leaves remainder 1, 2 and 3 respectively, is
a) 63
b) 61
c) 59
d) 57
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 4 – 1 = 3, 5 – 2 = 3, 6 – 3 = 3
∴ The required number = LCM of (4, 5, 6) – 3
= 60 – 3 = 57
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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