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📰 Check 9: need two multiples of 3, but in five consecutive, only one multiple of 3 unless spaced correctly (e.g., 3 and 6: 6 is divisible by 3, 3 by 3 → only one multiple of 3 unless 9 appears). Sequence 7–11: none divisible by 3 → product not divisible by 3? Wait: 9 is divisible by 3, but if no multiple of 3, like 4–8: no multiple of 3 → product \( 4 \times 5 \times 6 \times 7 \times 8 \)? Wait, 6 is included → divisible by 3. 📰 Any five consecutive integers must include at least one multiple of 3? No: e.g., 1–5: no multiple of 3? 1,2,3,4,5 → 3 is there. 4–8: 6 → yes. 7–11: 9 → yes. 8–12: 9 and 12 → yes. Actually: in any 5 consecutive integers, the distance is less than 6, so by pigeonhole, since residues mod 3 are 0,1,2, and 5 > 3, so at least one residue class must repeat or cover all? Actually, in any 3 consecutive, one divisible by 3; the span 5 covers at least one full residue cycle. Minimal case: the set must cover at least one multiple of 3. In fact, the maximum gap between multiples of 3 is 3, so 5 numbers span more than one cycle, so at least one number is divisible by 3. Similarly for 5: the gap is 5, so one number is divisible by 5. 📰 Thus, product always divisible by \( 2^3 = 8 \), \( 3 \), \( 5 \), so by \( \text{lcm}(8,3,5) = 120 \). 📰 Firestar Marvels Most Astonishing Moments Youve Been Missingcheck Them Out 6710861 📰 Stellar Dream 📰 Online Automobile Loan 3969852 📰 Louisiana Voodoo Fries The Shocking Ingredients Making Gourmets Ravedont Miss 2708849 📰 New Development Verizon Castro Valley Ca And People Are Shocked 📰 Fire Emblem Heroes Gamefaqs 4438068 📰 None Of Your Business Roblox 📰 4 Day Split Gym Program 9650150 📰 Your Smile Wont Stay Hidden Anymorediscover The Shocking Truth Behind The Price Of A Dental Cap The Hidden Cost No One Talks About Concealed Dental Expense Revealed Fina Smile Without Breaking The Bank No Its Not Freeyou Wont Believe What Price Tags Really Hide 9978916 📰 Admission Price To Cedar Point Amusement Park 4444304 📰 How Do You Play The New Skate 📰 Emergency Declaration Announcedheres What You Must Do Now 2967718 📰 Transform Your Dishes Instantlychiveon Is The Game Changer You Need 7773813 📰 1701 Rockville Pike 5565347 📰 Best Stock Trading Websites