Question

Gaurav and Saurabh both did their laundry today. Gaurav does laundry on every 6th day and Saurabh does laundry on every 9th day. How many days will it be until Gaurav & Saurabh both do the laundry on the same day again?

Answer 1

Gaurav does laundry on every 6th day, i.e. 6, 12, 18, 24, 30 and so on days from today.
Saurabh does laundry on every 9th day, i.e. 9, 18, 27, 36, 45 and so on days from today.
Here we saw that they meet after 18 days at the earliest.
Mathematically we say that 18 is the LCM of 6 & 9.
So, it will be 18 days until Gaurav and Saurabh both do the laundry on the same day.