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) 77
(b) 149
(c) 113
(d) 95
The correct answers to the above question in:
Answer: (d)
The difference between the divisor and the corresponding remainder is same in each case ie. 18 – 5 = 13, 27 – 14 = 13, 36 – 23 = 13
∴ Required number = (LCM of 18, 27, and 36 ) – 13
= 108 – 13 = 95
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Read more find lcm using formula Based Quantitative Aptitude Questions and Answers
Question : 1
Three men step off together from the same spot. Their steps measure 63 cm, 70 cm and 77 cm respectively. The minimum distance each should cover so that all can cover the distance in complete steps is
a) 6950 cm
b) 6930 cm
c) 9360 cm
d) 9630 cm
Answer »Answer: (b)
Required distance = LCM of 63, 70 and 77 cm.
= 6930 cm.
Illustration :
7 | 63, | 70, | 77 |
9, | 10, | 11 |
∴ LCM = 7 × 9 × 10 × 11
= 6930
Question : 2
From a point on a circular track 5 km long A, B and C started running in the same direction at the same time with speed of 2$1/2$ km per hour, 3 km per hour and 2 km per hour respectively. Then on the starting point all three will meet again after
a) 15 hours
b) 10 hours
c) 6 hours
d) 30 hours
Answer »Answer: (b)
A makes one complete round of the circular track in $5/{5/2}$ = 2 hours,
B in $5/3$ hours and C in $5/2$ hours.
That is after 2 hours A is at the starting point, B after $5/3$ hours and C after $5/2$ hours.
Hence the required time = LCM of 2, $5/3$ and $5/2$ hours
= ${\text"LCM of " 2, 5, 5}/ {\text"HCF of " 3, 2}$
= $10/1$ = 10 hours.
Question : 3
The smallest number, which when divided by 12 and 16 leaves remainder 5 and 9 respectively, is :
a) 29
b) 39
c) 41
d) 55
Answer »Answer: (c)
Using Rule 5,
When a number is divided by a, b or c, leaving remainders p, q or r respectively such that the difference between divisor and remainder in each case is the same
i.e., (a – P) = (b – q) = (c – r) = t (say) then that (least) number must be in the form of (k – t),
Where k is LCM of a, b and c
Here, 12 – 5 = 7, 16 – 9 = 7
∴ Required number = (L.C.M. of 12 and 16) – 7
= 48 – 7 = 41
Question : 4
The smallest number, which when divided by 5, 10, 12 and 15, leaves remainder 2 in each case; but when divided by 7 leaves no remainder, is
a) 91
b) 175
c) 182
d) 189
Answer »Answer: (c)
LCM of 5, 10, 12, 15
2 | 5, | 10, | 12, | 15 |
3 | 5, | 5, | 6, | 15 |
5 | 5, | 5, | 2, | 5 |
1, | 1, | 2, | 1 |
∴ LCM = 2 × 3 × 5 × 2 = 60
∴ Number = 60k + 2
Now, the required number should be divisible by 7.
Now, 60k + 2 = 7 × 8k + 4k + 2 If we put k = 3, (4k + 2) is equal to 14 which is exactly divisible by 7.
∴ Required number = 60 × 3 + 2 = 182
Question : 5
L.C.M. of $2/3, 4/9, 5/6$ is
a) $20/27$
b) $10/3$
c) $20/3$
d) $8/27$
Answer »Answer: (c)
Using Rule 2,
$\text"L.C.M of fractions" = \text"L.C.M.of numerators"/\text"H.C.F.of denominators"$
LCM = ${\text"LCM of " 2, 4, 5}/{\text"HCF of " 3, 9, 6}$= $20/3$
Question : 6
Four bells ring at the intervals of 5, 6, 8 and 9 seconds. All the bells ring simultaneously at some time. They will again ring simultaneously after
a) 24 minutes
b) 18 minutes
c) 12 minutes
d) 6 minutes
Answer »Answer: (d)
The LCM of 5, 6, 8 and 9 = 360 seconds = 6 minutes
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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