Multiples

When a number divides another number exactly, then the dividend is called a multiple of the divisor.

Ex- :

8 divides 32 exactly, so 32 is a multiple of  8.

Properties 

  1. Every non-zero number has an unlimited number of multiples.
  2. Every number is a multiple of  1.
  3. Every non-zero number is a multiple of itself.
  4.  0 is a multiple of every non-zero number.
  5. Every multiple of a non-zero number is either greater than or equal to the given number.
  6. The first multiple of the number is the number itself.

Lowest common multiple (LCM)

The LCM of some given numbers is the smallest common multiple.

Ex- :

Find the  \text{LCM} of 6 and  8.

6\ \rightarrow\  6,\ 12,\ 18,\ \boxed{24},\ 30,\ 36,\ 42,\ \boxed{48},\ 54,\ 60,\ 66,\ \boxed{72}\cdots

8\ \rightarrow\ 8,\ 16,\boxed{24},\ 32,\ 40,\ \boxed{48},\ 56,\ 64,\ \boxed{72}\cdots

Common multiples  =24,\ 48,\ 72,\cdots.

\text{LCM}=24 .

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