Question

What number am I ?
I am a two-digit even number.
I am a common multiple of $6$ and $7$.
I have a total of $8$ factors.

• A. $35$
• B. $42$
• C. $36$
• D. $84$

Answer 1

The correct option is B $42$

Let xy be a two digit number

Given xy have common multiple $6$ and $7$

$\Rightarrow xy=6\times 7\times y\times z$

$=42\times y\times z$

Also given it has $8$ factors.

Lets check for $42$ first

$42=21\times 2=2\times 21$

$=6\times 7=7\times 6$

$=14\times 3=3\times 14$

$=1\times 42=42\times 1$

$42$ has $8$ factors and common multiple of $6$ and $7$.