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The number which is divisible by 8, 15, and 21 is also divisible by the L.C.M. of the number.

The L.C.M. of 8, 15 and 21 is

\[8{\text{ }} = {\text{ }}2\; \times {\text{ }}2\; \times {\text{ }}2\]

\[15{\text{ }} = {\text{ }}3\; \times {\text{ }}5\]

\[21{\text{ }} = {\text{ }}3\; \times {\text{ }}7\]

L.C.M. \[ = {\text{ }}2\; \times {\text{ }}2\; \times {\text{ }}2\; \times {\text{ }}3\; \times {\text{ }}5\; \times {\text{ }}7{\text{ }} = {\text{ }}840\]

If we divide 110000 by 840, we will find out that it is not exactly divisible and we get 800 as remainder.

Thus the number nearest to 110000 but greater than 100000 which is exactly divisible by 840 i.e. divisible by 8, 15 and 21

\[ = {\text{ }}110000{\text{ }} - {\text{ }}800{\text{ }} = {\text{ }}109200\]

Hence 109200 is exactly divisible by 8, 15 and 21.

So, we have our answer as,

LCM, i.e. the least common multiple is the smallest positive number that is a multiple of two or more numbers.