Answer:
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.
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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
