Unit 3 sec 1.1

When you use a cash machine to withdraw money, it gives you options for the amount of money that it will dispense. The options might be

£20 £30, £40, £50, £100, £200.

  The amount multiples of £10.

In general, multiple of a natural number is the result of multiplying it by a natural number. For example, the multiples on 6 are 6, 12, 18, 24, 30, and so on. Because

1 × 6 = 6

2 × 6 = 12

3 × 6 = 18.

   In a way to think of the multiples of 6 is that they are the numbers into which 6 divides exactly. For example, 324 is a multiple of 6 because

324 ÷ 6 = 54, and 54 is a whole number

But 472 is not a multiple of 6 because

 472 ÷ 6 = 78.666 which is not a whole number

 Common multiples

work at these lists of depots due multiples of 6 and 8:

multiples of 6: 6, 12, 18, 24, 30, 36, 42, 48, 54, 60

multiples of 8: 8, 16, 24, 32, 40, 48, 56, 64, 72, 80.

  Notice that the number 24, appeared in both lists. We say that it is a common multiple of 6 and 8. There are other common multiple of 6 and the number 48 also appears in both lists, and the cellists were extended, then you would see that other numbers, for example, 72, 96 and 120, also appear in both lists. In fact, there are infinitely many common multiples of 6 and 8.

   A common multiple of two or more numbers is a number that is multiple of all of them. The laws common multiple (LCM) of two or more numbers is the smallest number that is a multiple of all of them. An alternative name common multiple is least common multiple.