Is there a lcm of 55 and 60

There's always an lcm of every integer.
The lcm of 55 and 60 is 660.

Yes.
The prime factorization of 55 is 5*11
The prime factorization of 60 is 2*2*3*5

To find the least common multiple of two numbers, all the numbers in the prime factorizations of each must be present in the prime factorization of the LCM.

In this case, you have to have two 2's because there are two 2's in the prime factorization of 60.
2*2*?

You also need a 3 because there is a 3 in the prime factorization of 60.
2*2*3*?

You need a 5 because it is in the prime factorization of both 55 and 60. You only need one because they both have one five in their prime factorization. If either had two fives in their prime factorization, then you would need two in the prime factorization of the LCM.
2*2*3*5*?

Lastly, you need an 11 because there is an 11 in the prime factorization of 55.
2*2*3*5*11=660