Your (a) is correct.

but how do i put that as my answer

240 = 2⁴ × 3 × 5
2750 = 2 × 5³ × 11


To make 240 a multiple of 2750, you must ensure that 240k has all the copies of prime factors that 2750 has.

The smallest k is attained when there are no extra/excess number of copies.


2750 has a 2 , which 240 already has in more than sufficient quantity (that 2⁴). So no need to multiply by 2.


2750 has a 5³. that's 3 copies of 5.
Since 240 only has 1 copy, you need to multiply 240 by 5, twice.


2750 has a 11, which 240 does not have. So you need to multiply 240 by 11 also.


240 × 5² × 11

= (2⁴ × 3 × 5) × 5² × 11

= 2³ × 3 × (2 × 5³ × 11)

= 2³ × 3 × 2750

= 8 × 3 × 2750

= 24 × 2750


So k = 5² × 11 = 25 × 11 = 275

Just write one above the other.

Actually if you realise, the above working for part c) was the same as finding the LCM for 240 and 2750.

Then finding what does 240 need to be multiplied by to get to this LCM.

So that k = 275

Edited for errors.

ohhhh i understand now !! thank you so much

No problem