What is the difference between the two smallest such integers

  27,720

Step-by-step explanation:

The smallest integer that will give a remainder of 1 for all divisors between 2 and 11 (inclusive) is 27,721. That value is ...

  LCM(2, 3, 4, 5, 6, 7, 8, 9, 10, 11) +1 = 27,720 +1 = 27,721

The next smallest integer that gives the same result is 27720 greater: 55,441.

The difference between the two smallest such integers is 27,720.

_____

The least common multiple (LCM) of the values in the range 2 .. 11 is the product of the primes in that range, each to the highest power it appears in any of the composite numbers in that range. That product is ...

  2³×3²×5×7×11 = 27,720

rick has $1400 and sally has $1500

step-by-step explanation:

to find amount of money rick has after 10 years :

principal = $1000 , time = 10 years , rate = 4% annually

to find amount of money sally has after 10 years :

her friend gives to pay her $50 per year, therefore money she has after 10 years = 50 × 10 = $500

also, sally gets $1000 after 10 years,

therefore, total amount of money sally has after 10 years = 500 + 1000 = $1500

so, after 10 years : rick has $1400 and sally has $1500