theme of "multiples of" studied in the 5th grade of secondary school.Its aim is to improve written and oral skills of mathematical calculations.This lesson introduces new concepts - "multiple number" and "splitters" technique worked through finding dividers and multiple integer, the ability to find different ways NOC.

This topic is very important.Knowledge of it can be applied in solving examples with fractions.To do this, you need to find a common denominator by calculating the least common multiple (LCM).

A fold is considered an integer that is divisible by without a trace.

18: 2 = 9

Every positive integer has an infinite number of multiples of numbers.It is itself considered to be the lowest.Multiple can not be less than the number itself.

task

necessary to prove that the number 125 is a multiple of the number 5. To do this, divide the first number on the second.If 125 is divided by five without a remainder, then the answer is positive.

all natural numbers can be divided into 1. Multiple divides for himself.

As we know, the number of fission called "dividend", "divider", "private".

27: 9 = 3, where

27 - divisible, 9 - divider, 3 - private.

multiples of 2, - those which, when divided by the two do not form a residue.They are all even.

multiples of 3 - is such that no residues are divided into three (3, 6, 9, 12, 15 ...).

example 72. This number is a multiple of three, because it is divided by 3 without a remainder (as is known, the number is divided by 3 without a remainder, if the sum of the digits is divided by three)

sum of 7 + 2 = 9;9: 3 = 3.

Is the number 11, a multiple of 4?

11: 4 = 2 (residue 3)

answer is no, because there is a balance.

common multiple of two or more integers - it is, which is divided by the number without a trace.

R (8) = 8, 16, 24 ...

K (6) = 6, 12, 18, 24 ...

K (6,8) = 24

LCM (least commonfold) are in the following manner.

For each number you need to write a separate line in multiples of - down to the same location.

NOC (5, 6) = 30.

This method is suitable for small numbers.

When calculating NOC meet special cases.

1. If it is necessary to find a common multiple of 2 numbers (e.g., 80 and 20), where one of them (80) is divisible by the other (20), this number (80) and is the smallest multiple of these twonumbers.

NOC (80, 20) = 80.

2. If two prime numbers have no common divisor, we can say that their NOC - is the product of these two numbers.

NOC (6, 7) = 42.

Consider the latest example.6 and 7 in relation to 42 are divisors.They share a multiple of no residue.

42: 7 = 6

42: 6 = 7

In this example, 6 and 7 are paired divisors.Their product is equal to a multiple of (42).

6x7 = 42

number is called simple if divisible only by itself and 1 (3: 1 = 3 3 3 = 1).The rest are called composite.

In another example, you need to determine whether the divider 9 with respect to the 42.

42: 9 = 4 (the remainder 6)

Answer: 9 is not a divisor of 42 because there is a balance in the response.

divider is different from a multiple of that divider - is the number by which divide natural numbers and fold itself is divided by this number.

greatest common divisor * a * and * b *, multiplied by their smallest fold, give themselves the product of the numbers * a * and * b *.

Namely: gcd (a, b) x LCM (a, b) = a x b.** **

General multiples of more complex numbers are in the following manner.

For example, to find the NOC 168, 180, 3024.

These numbers are decomposed into prime factors, written as a product of degrees:

2³h3¹h7¹ 168 = 180 =

2²h3²h5¹

3024 = 2⁴h3³h7¹

Then write down all the groundsdegrees with the greatest performance and multiply them:

2⁴h3³h5¹h7¹ = 15120

NOC (168, 180, 3024) = 15120.