### The LCM of two numbers is 100 the gcf of the numbers is 1 the sum of the numbers is 29 what are the numbers?

The numbers are 25 and 4 Explanation: If A and B are two whole numbers, the product of their LCM and GCF is equal to their product AB. So using this we have AB=100 and A+B=29 so A=29-B B(29-B)=100 This is a quadratic 29B-B2 -100=0 or B2 -29B+100=0 (B-25)(B-4)=0 So B=25 and 4. Now let's check The gcf 25 and 4 is 1 The LCM is 100