Random Puzzles 

Workings

Hint
One answer changes Warm to Worm.

Answer
WARM, WORM, WORK, CORK, COOK, COOL

or

WARM, WORM, WORD, WOOD, WOOL, COOL.

Workings

Hint
The second word is CORD.

Answer
COLD, CORD, WORD, WARD, WARM

or

COLD, CORD, WORD, WORM, WARM

or

COLD, CORD, CARD, WARD, WARM.

Workings

Hint
One of the names is MEL.

Answer
demi----     + john  = demijohn
---ple       + sam   = sample
absor---t    + ben   = absorbent
he---che     + ada   = headache
sc----r      + anne  = scanner
----ionaire  + bill  = billionaire
break---ce   + dan   = breakdance
monog---     + amy   = monogamy
-----incense + frank = frankincense
s---ly       + mel   = smelly

Workings

Hint
Try starting with the cube root of the number.

Answer
195 x 197 x 199.

Reasoning
Since we're after three numbers that multiply together, a good place to start is the cube root of 7,644,585, which is roughly 196.99.

Let's try dividing by the closest odd number to 196.99:

   7644585 ÷ 197 = 38805

We're now after whole divisors of 38,805, so trying either odd number either side of 197 might work.

Trying either 195 or 199 gives the answer.

Double-Checking
   195 x 197 x 199 = 7,644,585

Note
Trying the closest odd number to the cube root always works, and the other two numbers are the odd numbers either side.