model 2 find lcm of numbers Practice Questions Answers Test with Solutions & More Shortcuts
LCM & HCF PRACTICE TEST [5 - EXERCISES]
model 1 Basic formula of LCM & HCF
model 2 find lcm of numbers
model 3 find hcf of numbers
model 4 addition, subtraction, multiplication and division with lcm & hcf
model 5 lcm & hcf vs ratios
Question : 1 [SSC Section Officer 2007]
The least number, which is a perfect square and is divisible by each of the numbers 16, 20 and 24, is
a) 14400
b) 6400
c) 3600
d) 1600
Answer »Answer: (c)
The smallest number divisible by 16, 20 and 24
= LCM of 16, 20 and 24
| 2 | 16, | 20 | 24 |
| 2 | 8, | 10, | 12, |
| 2 | 4, | 5, | 6, |
| 2, | 5, | 3 |
∴LCM = 2×2×2×2×5×3
= $2^2$ × $2^2$ × 5 × 3
∴Required complete square number =$2^2$ × $2^2$ × $5^2$ × $3^2$ = 3600
Question : 2 [SSC Investigator 2010]
The smallest number, which, when divided by 12 or 10 or 8, leaves remainder 6 in each case, is
a) 66
b) 126
c) 186
d) 246
Answer »Answer: (b)
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 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
The smallest number divisible by 12 or 10 or 8
= LCM of 12, 10 and 8 = 120
⇒ Required number =120 + 6 = 126
Question : 3
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
Question : 4 [SSC CPO 2008]
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 : 5
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.
IMPORTANT quantitative aptitude EXERCISES
model 2 find lcm of numbers Shortcuts »
Click to Read...model 2 find lcm of numbers Online Quiz
Click to Start..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 …
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