Anne is a caring daughter. She visits her old parents after every 5 days. Tony her brother visits their parents after every 4 days. Each time the two siblings meet at their parent's house, they share a cake. On the 1st of January they shared a cake at their parent's house. On what day and a month will Anne and Tony be sharing their next cake at their parent's house?

Question

GPT-4o mini · Answer

To find out when Anne and Tony will next share a cake at their parent's house, we need to determine when both siblings will visit their parents on the same day again after January 1st.

Anne visits every 5 days, and Tony visits every 4 days. We need to find the least common multiple (LCM) of 5 and 4 in order to find the next day both will be there together.

The multiples of 5 are:

5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60...

The multiples of 4 are:

4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48...

The first common multiple in both lists is 20.

Now, we need to count 20 days from January 1st.

January has 31 days. Therefore, we can calculate:

January 1 + 20 days = January 21.

Thus, Anne and Tony will next share a cake at their parent's house on January 21st.