The LCM of two whole numbers is 45 times their HCF, and the LCM and the HCF together add up to 1150. If one of the numbers is 125, what is the other?

Call the HCF $h$, so the LCM is 45$h$ and $h+45h=46h=1150$, giving $h=25$ and LCM = 1125. The product of two numbers always equals HCF × LCM, so the other number is $25\times 1125÷125=225$. Checking: $125=5^3$ and $225=3^2\times 5^2$, so the HCF is $5^2=25$ and the LCM is $3^2\times 5^3=1125$ ✓. The traps report the wrong quantity — 1125 is the LCM and 25 is the HCF — while 1025 comes from subtracting the given number from the total (1150 − 125) instead of using the product rule.