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48 questions · timed · auto-graded

Question 12 Marks
The product of two two-digit numbers is 765 and their HCF is 3. What is their LCM ?
Answer
Here, $HCF =3$, Product of the given numbers $=765$ Now, HCF x LCM = Product of the given numbers
$
\begin{aligned}
& \therefore 3 \times LCM =765 \\
& \therefore LCM =\frac{765}{3}=255
\end{aligned}
$
$\therefore$ The LCM of the two two-digit numbers is 255 .
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Question 22 Marks
The LCM and HCF of two numbers are 432 and 72 respectively. If one of the numbers is 216, what is the other ?
Answer
Here, LCM = 432, HCF = 72, First number = 216
First number x Second number = LCM x HCF
∴ 216 x Second number = 432 x 72

∴ Second number =$\frac{432 \times 72}{216}=432 \times \frac{72}{216}=432 \times \frac{1}{3}=144$

∴ The other number is 144.

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Question 82 Marks
Find the HCF and LCM.21,49,84
Answer
21 = 3 x 7
49 = 7 x 7
84 = 2 x 42
= 2 x 2 x 21
= 2 x 2 x 3 x 7
∴ HCF of 21, 49 and 84 = 7
∴ LCM of 21, 49 and 84 = 7 x 3 x 7 x 2 x 2
= 588
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Question 92 Marks
Find the HCF and LCM.23,69
Answer
23 = 23 x 1
69 = 3 x 23
∴ HCF of 23 and 69 = 23
∴ LCM of 23 and 69 = 23 x 3
= 69
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Question 102 Marks
Find the HCF and LCM.17, 102, 170
Answer
17 = 17 x 1
102 = 2 x 51
= 2 x 3 x 17
170 = 2 x 85
= 2 x 5 x 17
∴ HCF of 17, 102 and 170 = 17
∴ LCM of 17, 102 and 170 = 17 x 2 x 3 x 5
= 510
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Question 112 Marks
Find the HCF and LCM.32,16
Answer
32 = 2 x 16
= 2 x 2 x 8
= 2 x 2 x 2 x 4
= 2 x 2 x 2 x 2 x 2
16 = 2 x 8
= 2 x 2 x 4
= 2 x 2 x 2 x 2
∴ HCF of 32 and 16 = 2 x 2 x 2 x 2
= 16
∴ LCM of 32 and 16 = 2 x 2 x 2 x 2 x 2
= 32
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Question 122 Marks
Find the HCF and LCM. : 14,28
Answer
i. 14 = 2 x 7
28 = 2 x 14
= 2 x 2 x 7
∴ HCF of 14 and 28 = 2 x 7
= 14
LCM of 14 and 28 = 2 x 2 x 7
= 28
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Question 232 Marks
Find HCF of The Following : $777,315,588$
Answer

Image

777 = 3 × 7 × 37
315 = 3 × 3 × 5 × 7
588 = 2 × 2 × 3 × 7 × 7
HCF of 777, 315 and 588 = 3 × 7
HCF of 777, 315 and 588 = 21

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Question 242 Marks
Find HCF of The Following : 56,57
Answer

Image

56 = 2 × 2 × 2 × 7 × 1
57 = 3 × 19 × 1
HCF of 56 and 57 = 1

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Question 252 Marks
Find HCF of The Following : 57, 75, 102
Answer

Image

57 = 3 × 19
75 = 3 × 5 × 5
102 = 2 × 3 × 17
HCF of 57, 75 and 102 = 3

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Question 262 Marks
Find HCF of The Following : $42,45,48$
Answer

Image

42 = 2 × 3 × 7
45 = 3 × 3 × 5
48 = 2 × 2 × 2 × 2 × 3
HCF of 42,45 and 48 =3

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Question 282 Marks
Find HCF of The Following : $18,32,48$
Answer

Image

18 = 2 × 3 × 3
32 = 2 × 2 × 2 × 2 × 2
48 = 2 × 2 × 2 × 2 × 3
HCF of 18, 32 and 48 = 2

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Question 292 Marks
Find HCF of The Following : 16,27
Answer

Image

∴ 16 = 2 × 2 × 2 × 2 × 1
27 = 3 × 3 × 3 × 1
∴ HCF of 16 and 27 = 1

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Question 302 Marks
Find HCF of The Following : $40,60,75$
Answer

Image

40 = 2 × 2 × 2 × 5
60 = 2 × 2 × 3 × 5
75 = 3 × 5 × 5
HCF of 40, 60 and 75 = 5

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Question 312 Marks
Find HCF of The Following : 56,32
Answer

Image

56 = 2 × 2 × 2 × 7
32 = 2 × 2 × 2 × 2 × 2
HCF of 56 and 32 = 2 × 2 × 2
HCF of 56 and 32 = 8

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Question 452 Marks
Which of the following are pairs of co-primes ? : 27,15
Answer
Factors of 27: 1, 3, 9, 27
Factors of 15: 1, 3, 5, 15 .
∴ Common factors of 27 and 15 : 1,3
∴ 27 and 15 are not a pair of co-prime numbers.
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Question 462 Marks
Which of the following are pairs of co-primes ? : 17,19
Answer
Factors of 17: 1, 17
Factors of 19: 1, 19
∴ Common factors of 17 and 19: 1
∴ 17 and 19 are a pair of co-prime numbers.
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Question 472 Marks
Which of the following are pairs of co-primes ? : 4,5
Answer
Factors of 4: 1, 4
Factors of 5: 1, 5
∴ Common factors of 4 and 5: 1
∴ 4 and 5 are a pair of co-prime numbers.
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Question 482 Marks
Which of the following are pairs of co-primes ? : 8,14
Answer
Factors of 8: 1, 2, 4, 8
Factors of 14: 1, 2, 7, 14
∴ Common factors of 8 and 14: 1,2
∴ 8 and 14 are not a pair of co-prime numbers.
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2 Mark Question - Maths STD 7 Questions - Vidyadip