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) 9995
(b) 9980
(c) 9960
(d) 9990
The correct answers to the above question in:
Answer: (c)
Using Rule 8,
Greatest n digit number which when divided by three numbers P, Q, R 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 P, Q, R.
LCM of 10, 15 and 20 = 60
Largest 4-digit number = 9999
∴ 166$39/60$ = 9999
∴ Required number = 9999 – 39
= 9960
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Read more find lcm using formula Based Quantitative Aptitude Questions and Answers
Question : 1
The number nearest to 43582 divisible by each of 25, 50 and 75 is :
a) 43550
b) 43600
c) 43650
d) 43500
Answer »Answer: (c)
LCM of 25, 50 and 75 = 150
On dividing 43582 by 150, remainder = 82
290$82/150$ = 43582
∴ Required number = 43582 + (150 – 82)
= 43650
Question : 2
The LCM of four consecutive numbers is 60. The sum of the first two numbers is equal to the fourth number. What is the sum of four numbers?
a) 24
b) 21
c) 14
d) 17
Answer »Answer: (c)
| 2 | 60 |
| 2 | 30 |
| 3 | 15, |
| 5 |
∴ 60 = 2 × 2 × 3 × 5
i.e., Numbers = 2, 3, 4 and 5
∴ Required sum = 2 + 3 + 4 + 5 = 14
Question : 3
The least number which when divided by 16, 18, 20 and 25 leaves 4 as remainder in each case but when divided by 7 leaves no remainder is
a) 18004
b) 18002
c) 18000
d) 17004
Answer »Answer: (a)
LCM of 16, 18, 20 and 25 = 3600
∴ Required number = 3600K + 4 which is exactly divisible by 7 for certain value of K.
When K = 5,
number = 3600 × 5 + 4
= 18004 which is exactly divisible by 7.
Question : 4
The least perfect square, which is divisible by each of 21, 36 and 66 is
a) 231444
b) 213444
c) 214434
d) 214344
Answer »Answer: (b)
LCM of 21, 36 and 66
∴ LCM = 3 × 2 × 7 × 6 × 11
= 3 × 3 × 2 × 2 × 7 × 11
∴ Required number
= $3^2 × 2^2 × 7^2 × 11^2$
= 213444
Question : 5
The smallest perfect square divisible by each of 6, 12 and 18 is
a) 36
b) 108
c) 144
d) 196
Answer »Answer: (a)
The LCM of 6, 12 and 18 = 36 = $6^2$
Question : 6
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
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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