24: Fill & Download for Free

Start by finding the least common multiple of those four numbers. One way to do this is to factorise each of them into prime numbers and pick the number which has all of the factors as many times as necessary16 = 2×2×2×218 = 2×3×324 = 2×2×2×330 = 2×3×5So we need four 2×2×2×2 for sixteen, another 3×3 for 18—these will be enough for 24—and a further 5 for 30. So the least common multiple is 2×2×2×2×3×3×5 = 720.Now multiply 720 by the smallest number that results in 10,000 or greater. 720×14 = 10,080.So the answer is 10,080, which is 16×630, 18×560, 24×420, or 30×336.

Hi..Over the last couple of years, Germany has become one of the top 3 destinations for many students willing to pursue their Master's program, thanks to the subsidized cost of education provided by the German government.The cost subsidized by the government is mainly due to the fact that Germany is projected to face a significant shortage of skilled labor force in the area of STEM over the next 5-10 years. So, if anybody plans to make a career out in Germany, then Master's would be a very good entry point.Most of the universities offer free education (i.e subsidized education). Assuming that you have sufficient knowledge about the procedure of applying and obtaining a VISA for studying in Germany (else, the following thread would be helpful : What is the procedure for pursuing an MS in germany?), I would directly come to actual cost scenario.The costs can be broken down into 2 parts :1) Education costYou need to pay a semester fee contribution which may vary between 170 Euros to 550 Euros a semester depending on the university. This would also cover your transportation costs within a certain radius from the university (say 20kms or more ) for the entire semester.If you take an average of 300 Euros, you pay 1200 Euros over your entire two year Master's program as semester fees.2) Living CostAccomodation : Students usually live in Flatshares, where-in they share the living area + kitchen + bathroom, while they get a private room for studies, sleep and other personal activities. These flatshares cost around 170 Euros to 400 Euros depending on the location. Eg: Frankfurt (200-250 Euros), Darmstadt (230-300 Euros), Stuttgart (230-330 Euros), Munich (300 - 400 Euros), Kaiserslautern (170 - 230 Euros), Berlin (150-250 Euros).Health Insurance : Students are obligated to have compulsory public health insurance that would cost around 80 euros a month.Food and Groceries : On a monthly basis, the groceries would cost around 80-100 euros for a comfortable lifestyle. If you eat regularly at the college canteen, add another 50 Euros to your monthly bill.Telephone : A good prepaid/postpaid plan with data would cost you anywhere between 10-20 Euros on a monthly basis.Others : Apart from the above mandatory expenses, some of the following expenses based on one's different lifestyle habits are listed belowIf you party on a regular basis involving drinks, entry to pubs and cigars, add another 60 to 100 Euros on your monthly bills.A meal in the college canteen would cost you 2.5 to 5 Euros. A meal or a dinner in a restaurant would cost you between 6 to 20 euros.Clothing : Clothing is not expensive in Germany. You get very good offers every month. You could find T-shirts between 5 to 25 Euros, Trousers between 19 to 65 euros, Formal shirts between 19 to 39 Euros, Jackets between 25 to 300 Euros and etc.Trips : If you love travelling and exploring places, then Europe is the right destination for you. From Frankfurt, you can drive to Switzerland (Zurich) within 4 hours, Austria in 4 hours, Poland (Warsaw ) in 7hours, France (Paris) in 6 hours, Holland (Amsterdam) in 7 hours and catch a 2 to 3 hour flight to Rome/Barcelona/Portugal/UK/ Norway/ Copenhagen etc. As a student, you would work out in a smart way to visit these places in the most economical manner ;-)Hence adding up all the mandatory expenses over a month would add up to Accomodation + Health Insurance + Food and Groceries + Telephone = 280 (averaged) + 80 + 105 (averaged) + 15 (averaged) = 480 Euros a month. Assume that you spend another 60-80 Euros every month ( excluding trips ) that would involve clothing, lunch/dinner at a restaurant, entry to a pub etc. So your monthly expenditure would be 480 + 80 = 560 Euros a month.Adding up the above, we arrive at 1200 Euros (University Semester fee for 24 months) + 560 *24 (Living Expenses for 24 months), we get 14640 Euros or lets round off to 15000 Euros to complete your Master's. So, all the very best for your Master's !!(Taking up a part-time job during your studies would further reduce your expenses.)I guess this information gives you the basic idea.Thank you

CHECK EDITED《 1,355,841,024 》For last 10 digits , calculate to mod 10^10 or 10km① 2,001,003,001× 3,001,001,002=(2km+1m+3k+1)×(3km+1m+1k+2)≡ (4+1+3+3)km+(2+3+1)m+(6+1)k+(2)≡ (10km+1km)+6m+7k+2)noting that 10km ≡0 (mod10km) ,it is ′cast out′ .≡ 1km+6m+7k+2②N²≡(1km+6m+7k+2)²≡(7k)²+(2)²+2{(1km×2)+(6m×7k)+(6m×2)+(7k×2)}...this step will be skipped hereinafter .≡ (4+84)km+(49+24)m+(28)k+(4)≡80km+8km+73m+28k+4≡8,073,028,004③ N^4≡(8km+70m+3m+20k+8k+4)²≡(64+48)km+(400+64+560+24+320)m+(160+64)k+(16)≡(110+2)km+(1km+368m)+224k+16≡3km+368m+224k+16≡3,368,224,016④N^8≡(3km+300m+60m+8m+200k+20k+4k+10+6)²≡(36+6+3+1+64+8+1)km+(400+16+600+200+720+160+96+600+4+2+160)m+(400+400+240+80+48)k+(100+36+120)≡(110+9)km+(2km+968m)+(1m+168k)+256≡11km+969m+168k+256≡1,969,168,256≡2km-31m+168k+256⑤N^10≡(2km-30m–1m+100k+70k-2k+200+50+6)×(8km+70m+3m+20k+8k+4)≡(48+14-6-20+2+1-8+8)km+(600+150+18+400-40+4+1+800+560–16+1-120-4)m+(120+600+400+48+400+280-8)k+(800+224)≡39km+2,354m+1840k +1024≡41km+355m+841k+24≡ 1,355,841,024