two cruise ships sail from NY to FL.ONE ship make the round trip in 8 days.the other ship make the round trip in 10 days.both ships sail from ny today.which is the fewest number of days before both ships will sail again from newyork on the same day?

LCM(8,10) = 40

What is the least common multiple of 8 and 10?

To find the fewest number of days before both ships will sail again from New York on the same day, we need to determine the least common multiple (LCM) of the two round trip times, which are 8 days and 10 days.

To find the LCM, we can use the prime factorization method:

Step 1: Prime factorize both numbers:
- The prime factorization of 8 is 2^3.
- The prime factorization of 10 is 2 * 5.

Step 2: Determine the common prime factors and their highest powers:
- The common prime factor is 2, with the highest power being 3.
- There are no other common prime factors.

Step 3: Multiply the common prime factors by their highest powers:
- 2^3 * 5 = 8 * 5 = 40.

Therefore, the least common multiple (LCM) of 8 and 10 is 40.

Hence, both ships will sail again from New York on the same day after 40 days.