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MATHS [2 Mark Question Answer]

HCF and LCM · ICSE STD 6 (ICSE - English Medium). 11 questions.

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[2 Mark Question Answer]

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11 questions · timed · auto-graded

Question 12 Marks
Find the L.C.M. of $140$ and $168.$ Use the L.C.M. obtained to find the H.C.F. of the given numbers.
Answer
Numbers are $140$ and $168$
L.C.M. of $140$ and $168$
$2$ $140,$ $168$
$2$ $70,$ $84$
$7$ $35,$ $42$
  $5,$ $6$
$=2 \times 2 \times 7 \times 5 \times 6=840$
$\text { H.C.F. }=\frac{1 \text { st number } \times 2 \text { nd number }}{\text { L.C.M. }}$
$=\frac{140 \times 168}{840}$
$=28$
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Question 22 Marks
Find the largest number that can divide 28 and 42 completely.
Answer
We know that the largest number which can divide 28 and 42 completely will be their H.C.F.

H.C.F. of 28 and 42 = 14
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Question 32 Marks
The product of the H.C.F. and the L.C.M. of two numbers is 1152. If one number is 48, find the other one.
Answer
We know that:
Product of two numbers $=$ Product of their H.C.F. and L.C.M.
$\Rightarrow 1$ st number $\times 2$ nd number $=$ Product of their H.C.F. and L.C.M.
$\Rightarrow 48 \times 2$ nd number $=1152$
$\Rightarrow 2$ nd number $=\frac{1152}{48}=24$
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Question 42 Marks
The product of two numbers is $12096$ and their H.C.F. is $36.$ Find their L.C.M.
Answer
We know that
Product of two numbers $=$ Product of their H.C.F. and L.C.M.
$\Rightarrow 12096=36 \times \text { L.C.M. }$
$\Rightarrow \text { L.C.M. }=\frac{12096}{36}=336$
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Question 52 Marks
The product of the two numbers is $19,200$ and their H.C.F. is $40.$ Find their L.C.M.
Answer
$\text { L.C.M. }=\frac{\text { Product of number }}{\text { H.C.F }} $
$\text { Product of number }=19,200$
$\text { H.C.F. }=40$
$\therefore \text { L.C.M }=\frac{19,200}{40}=480$
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Question 62 Marks
The product of two numbers is 432 and their L.C.M. is 72. Find their H.C.F.
Answer
Product of two numbers = Product of their L.C.M. and H.C.F.
Here, the product of two number $=432$
L.C.M. $=72$
H.C.F. $=\frac{432}{72}=6$
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Question 72 Marks
Using the common factor method, find the H.C.F. of 27 and 75
Answer
$F_{27}=1,3,9,27$
$F_{75}=1,3,5,15,25,75$
Common factors between 27 and $75=1,3$ H.C.F. of 27 and $75=3$
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Question 82 Marks
Using the common factor method, find the H.C.F. of 25 and 20
Answer
$F_{25}=1,5,25$
$F_{20}=1,2,4,5,10,20$
Common factors between 25 and $20=1,5$
H.C.F. of 25 and $20=5$
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Question 92 Marks
Using the common factor method, find the H.C.F. of 16 and 35
Answer
$F_{16}=1,2,4,8,16$
$F_{35}=1,5,7,35$
Common factors between 16 and $35=1$
H.C.F. of 16 and $35=1$
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