How to find an NOC?

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How to find an NOC?

For many students, the mathematician is one of the mostproblem subjects. Although in fact it is very interesting, though not an easy science. In it, the main thing is not only to memorize, but also to understand what has been learned. Today we suggest you to understand the question of how to find NOC numbers.

The concept of NOCs

First we need to understand what is multiple. A multiple is a number that is divided by a given number completely, i.e. without a remnant. For example, for 4 times, 4, 8, 16, and so on. A common multiple is a number divided by each of these numbers without a remainder. If we take the numbers 8 and 16, then their common multiples - 16, 32, 48, 64, etc.

The smallest common multiple, or LCM, of several numbers is the smallest natural number, which itself can be divided into each of these numbers without a remainder. For the 8 and 16 already considered, this number is 16.

Problem Solving

In order to find the LCM of two numbers, do the following:

Expand the data in a number problem into simplemultipliers, i.e. prime numbers (they only divide by one and into itself), which when multiplied give the original. To do this, separate the sheet with a vertical line. In the first column write down this number, and in the second - the smallest common divisor. The private of these numbers is written in the first column. And thus divide the number until you get the unit.

Suppose you want to find LCMs 21 and 48. We decompose them:

In the line, write down all the multipliers of the largest number, and below it the others. Emphasize among the simple multipliers of a smaller number those that have not entered into more.

• 48: 2, 2, 2, 2, 3, 1
• 21: 3, 7, 1

Now multiply the larger number by the missing multiplier - and get the answer.

• NOC (21, 48) = 48 x 7 = 336.

If you need to find an LCM for three or more numbers, then the sequence of your actions is the same, but you must take into account the multipliers of all numbers.