Question

Glenn found a number with an interesting property.

When he divides the number by numbers ranging from 2 to 10, he gets the remainder as 1,2,3,4,5,6,7,8, and 9 respectively.

Find the smallest number which has this peculiar property.

Answer 1

Answer:

Take the LCM (Least Common Multiple) of numbers 2 to 10. Then, subtract 1 from the resulting number and you’ll have your answer.

LCM of numbers 2 to 10 = 8*9*7*5 = 2520

After subtracting 1, it becomes 2519.

This is the smallest number that satisfies the above criteria.

Answer 2

Answer:

2519

Step-by-step explanation:

Number= x

Property= Divisible by all numbers from 2 to 10 leaving a remainder of 1

What we need to find: The smallest number which has this property

Smallest number: LCM

LCM of 2,3,4,5,6,7,8,9,10=

2=1x2

3=1x3

4=2x2

5=1x5

6=2x3

7=1x7

8=2x2x2

9=3x3

10=2x5

LCM=1x2x3x2x5x7x2x3

          2   x  6  x 35 x6

               12      x 210

=2520

LCM of numbers from 2 to 10=2520

Remainder?= Yes

Answer= LCM-1

2520-1

=2519