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) 63
(b) 61
(c) 59
(d) 57
The correct answers to the above question in:
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
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Read more find lcm using formula Based Quantitative Aptitude Questions and Answers
Question : 1
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 : 2
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 : 3
The smallest square number divisible by 10, 16 and 24 is
a) 3600
b) 2500
c) 1600
d) 900
Answer »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
Question : 4
The traffic lights at three different road crossings change after 24 seconds, 36 seconds and 54 seconds respectively. If they all change simultaneously at 10 : 15 : 00 AM, then at what time will they again change simultaneously?
a) 10 : 22 : 12 AM
b) 10 : 17 : 02 AM
c) 10 : 18 : 36 AM
d) 10 : 16 : 54 AM
Answer »Answer: (c)
LCM of 24, 36 and 54 seconds
= 216 seconds
= 3 minutes 36 seconds
= 10 : 18 : 36 a.m.
Question : 5
The smallest number, which when increased by 5 is divisible by each of 24,32, 36 and 564, is
a) 427
b) 4320
c) 859
d) 869
Answer »Answer: (c)
Required number = (LCM of 24, 32, 36 and 54) – 5
Now,
| 2 | 24, | 32, | 36, | 54 |
| 2 | 12, | 16, | 18, | 27 |
| 2 | 6, | 8, | 9, | 27 |
| 3 | 3, | 4, | 9, | 27 |
| 3 | 1, | 4, | 3, | 9 |
| 1, | 4, | 1, | 3 |
LCM = 2 × 2 × 2 × 3 × 3 × 3 × 4 = 864
∴ Required number = 864 – 5
= 859
Question : 6
The least number which when divided by 5, 6, 7 and 8 leaves a remainder 3, but when divided by 9 leaves no remainder is
a) 3363
b) 2523
c) 1683
d) 1677
Answer »Answer: (c)
The LCM of 5, 6, 7 and 8 = 840
∴ Required number = 840 k + 3 which is exactly divisible by 9 for some value of k.
Now, 840 k + 3 = 93 × 9 k + (3k + 3)
When k = 2, 3k + 3 = 9, which is divisible by 9.
∴ Required number = 840 × 2 + 3 = 1683
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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