1. **State the problem:** We have two investments that pay out every 4 years and every 6 years respectively. We want to find out after how many years both investments will pay out money together and how much total money will be paid then. 2. **Find the interval when both payouts coincide:** The payments coincide at multiples of both 4 and 6 years. This is the least common multiple (LCM) of 4 and 6. $$\text{LCM}(4,6)=12.$$ So every 12 years, both investments pay out on the same year. 3. **Calculate total payout after 12 years:** - First investment pays £225 every 4 years so it pays at years 4, 8, 12. - Second investment pays £350 every 6 years so it pays at years 6, 12. At year 12, both pay out simultaneously. 4. **Compute total payout at year 12:** - First investment payout = £225 - Second investment payout = £350 - Total payout at year 12 = £225 + £350 = £575 **Final answer:** Both investments pay out together every 12 years, and the total payout then is £575.