What is the least value that J can have to be divisible both by 12 and 10?
Obviously, the LCM of 10 and 12 which is 60
Is 60 divisible by 24? No.

What is the next number after 60 that is divisible by 12 and 10?? 120
Is 120 divisible by 24? Yes

So what is the value of J? 60 or 120? We dont know. Thus the answer is a "Maybe"

Thank you very much, but I am still not sure I understand this fully: why can' t I reduce 12 and 10 to their prime factors and see whether by multiplying these I can get 24? If I do this, the prime numbers I get are 2, 2, 2, 3, 5, though I know (by looking at the answer) that this is one 2 too many. Why is this, and what method should I use for these sorts of questions in future? I know this has somethng to do with repeated primes...

Thanks again!

You are confusing concepts over here.

The concept of "repeated prime" is useful when you want to find the LCM of 2 or more numbers

When you split numbers into their prime factors, the shortest way to finding their LCM is to take the primes that have the highest powers
12 = 2x2x3 = (2^2) x 3
10 = 2x5

In the above case, the highest power of 2 is 2^2 so you consider 2^2. 3 and 5 only have a power of 1
So your LCM = 2^2 x 3 x 5 = 60

Thanks so so much - that is really helpful. Got it!