OK. You're getting there. But your last step isn't correct.
Let me rewrite your prime factorizations a bit nicer first:
15=3⋅5
39=3⋅13
30=2⋅3⋅5
21=3⋅7
70=2⋅5⋅7
Now you wrote that the lcm is
53⋅34⋅13⋅22⋅72. This is incorrect. What you have written down is simply the
product of the given numbers, ie. this is the same as just multiplying all the original numbers together. Do you see why?
Although the product is a common multiple of all the given numbers, it is usually not the
least common multiple. To get the least common multiple you only take each prime factor that appears once, and you take the highest power of that prime that appears in any of the factorizations. For example, the highest power of
2 that appears is simply
2. So you would use
2 in the lcm, not
22. See if you can write down the answer now.
Side note: When writing down prime factorizations it is best to write the primes in increasing order. There is a good theoretical reason for this, but most importantly for you it will be more readable and you will be less likely to make careless errors. So for example notice that I write
15=3⋅5 as opposed to
15=5⋅3
The first of these is known as
canonical form. The word "canonical" is just a sophisticated synonym for "natural"