PG Mathematics (HAGGEP) (a) Douglas goes to the communily centre once every 4 days. Lauren \( \mathrm{Bl}_{\mathrm{m}} \). If they last met each ons. to the community centre once every 6 days. If they last met each othen at the community centre on \( 1^{\text {st }} \) August, on which date wirt trey meet an the community centre again? (b) There are 138 pages in a textbook. What is the total number of digits on all the pages of the textbook? Look tor the fowest cormmon mlimple for ( part a) List down the number of pages for page range 1-9, 10-99 and 100-138 (part b)

To figure out when Douglas and Lauren will meet again at the community center, you need to find the least common multiple (LCM) of their visiting cycles. This is where the fun begins! Douglas visits every 4 days, and Lauren every 6 days. The LCM of 4 and 6 is 12. So, 12 days after August 1st lands us on August 13th. They’ll meet again on that day—mark your calendars! Now, about the pages in the textbook! Let's categorize the pages. For pages 1-9, there are 9 pages, each with 1 digit, contributing a total of 9 digits. For pages 10-99, there are 90 pages (from 10 to 99), each with 2 digits. This gives us 90 * 2 = 180 digits. Finally, for pages 100-138, there are 39 pages, each having 3 digits, contributing 39 * 3 = 117 digits. Adding them up, you get 9 + 180 + 117 = 306 digits in total. That’s a lot of counting!