Match the item in left column with corresponding items in right column.

Column 1 Column 2

HCF of $108$ and $117$

$1$

LCM of $15$ and $35$

$84$

$HCF \times LCM$ of $12$ and $7$

$9$

$2 -$ digit perfect number

$28$

HCF of $23$ and $24$

$105$

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Solution

A) HCF of $108$ and $117$
Factors of $108$ is $1, 2, 3, 4, 6, 8, 9, 12, 18, 27, 36, 54, and 108 .$
Factors of $117$ is $1, 3, 9, 13, 39, 117$
HCF of $108$ and $117$ is $9 .$

B) LCM of $15$ and $35 = ?$
Prime factorisation of $15 = 3 \times 5$
Prime factorisation of $35 = 5 \times 7$
LCM of $15$ and $35 = 105$

C) $HCF \times LCM$ of $12$ and $7$ is $12 \times 7 = 84$

D) Since as we know that perfect number are the numbers whose sum of all factors is equal to the twice of that number.
$2 -$ digit perfect number is $28$ because sum of its factors $1 + 2 + 4 + 7 + 14 + 28 = 56$ which is the double of $28$ .
Hence , $2 -$ digit perfect number is $28$
E) HCF of $23$ and $24$ is $1 .$

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