Lcm из 10 последовательных чисел

I am attaching my codes with the question. I have used the logic :
I have first found all the prime numbers in the 10 consecutive numbers starting from 1. Used them to divide each number in the range of the 10 consecutive numbers starting from 1. Then i have counted their power and then have displayed the product.

I know that I am wrong at the last step but I want to know whether I can use my initial logic to solve this problem. Other logics are equally welcomed. Thank You in advance.

count = 0
product = 1
num = 0
c1 = 0
for i in range(1,10):
    i += 1
    for n in range(2,i):
        num = i%n
        n += 1
        if num == 0:
            count += 1
        else:
            continue
    if count == 0:
            prime = i
    else:
            continue
    for x in range(2,10):
            if x%prime == 0:
                while x%prime==0:
                    c1 += 1
                product *= (prime**c1)
print(product)