Lakshya Education MCQs

Question: Which of the following represents the correct prime factorisation of 272?
Options:
A.22×32×13
B.24×17
C.33×13
D.2×3×7×11
Answer: Option B
: B

272 can be factorised as following:


Thus 272 = 24×17

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More Questions on This Topic :

Question 1. If a = 23×3, b = 2×3×5, c = 3n×5 and LCM (a, b, c) = 23×32×5, then n = ?

(Here, n is a natural number)
  1.    1
  2.    2
  3.    3
  4.    4
Answer: Option B
: B

Given: a = 23×3
b = 2×3×5
c = 3n×5
LCM (a, b, c) = 23×32×5 ... (1)
Since, to find LCM we need to take the prime factors with their highest degree:
LCM will be23×3n×5 ... (2) (n1)
On comparing we get,
n = 2
Question 2. Let N be the greatest number that will divide 1305, 4665 and 6905, leaving the same remainder in each case. The sum of the digits in N is:
  1.    4
  2.    5
  3.    6
  4.    7
Answer: Option A
: A

Since the remainder is same in each case, hence we will use the following formula
H.C.F (x, y, z) = H.C.F of (x -y), (y- z), ( z-x)

N = H.C.F. of (6905 - 4665), (4665 - 1305), and (6905 - 1305)
= H.C.F. of 2240, 3360and 5600 HCF of 5600 and 3360: 5600=3360×1+2240
3360=2240×1+1120
2240=1120×2+0
HCF of5600 and3360= 1120 Now, HCF of 2240 and 1120 = 1120
So, the HCF of (3360, 2240 and 5600) = N = 1120 Sum of digits in N = (1 + 1 + 2 + 0) = 4
Question 3. A number when divided by 6 leaves a remainder 3. When the square of the number is divided by 6, the remainder is 3.
  1.    True
  2.    False
Answer: Option A
: A

Let the number be x
Given: x=6q+3 where q is a whole number.

Squaring both sides, x2=(6q+3)2
x2=36q2+36q+9
x2=6(6q2+6q+1)+3
When x2 is divided by 6, then the remainder is 3.
Question 4. The greatest four digits number which is divisible by 15, 25, 40 and 75 is
  1.    9000
  2.    9400
  3.    9600
  4.    9800
Answer: Option C
: C

L.C.M of15, 25, 40 and 75 is 600 Largest 4 digits number is 9999. When 9999 is divided by 600, the remainder will be 399. So, the required number is (9999 - 399) = 9600
Question 5. If 132300=22×33×52×ab, then which of the following is true ?
  1.    a=2b     
  2.    a+b=8
  3.     LCM of a and b is 14.        
  4.    a=b
Answer: Option C
: C

132300=22×33×52×ab
By fundamental theorem of arithmetic, 132300 can be written as 22×33×52×72.
On comparison, we geta=7 and b=2.
LCM of 7 and 2 is 14.
Question 6. If the HCF of 60 and 168 is 12, what is the LCM?
  1.    480
  2.    240
  3.    840
  4.    420
Answer: Option C
: C

Given: HCF of 60 and 168 = 12
Product of two given numbers = Product of their HCF and LCM
60 × 168 = 12 × LCM
LCM = 60×16812
LCM = 840
LCM of 60 and 168 is 840.

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