# OEF gcd --- Introduction ---

This module actually contains 18 exercises on gcd (greatest commun divisor) and lcm (lowest commun multiple) of integers.

### gcd and existence

Do there exist two integers m, n such that:

gcd(m,n)=, mn= ?

Compute gcd(,).

Compute gcd(,,).

Compute gcd(,).

### gcd and lcm

Find the positive integer n such that:

gcd(n,)=, lcm(n,)=.

### gcd and lcm II

Find two positive integers m and n, other than and , such that:

gcd(m,n)=, lcm(m,n)=.

You can enter the two integers in any order.

### gcd and lcm III

Find two positive integers m and n, other than and , such that:

gcd(m,n)=, lcm(m,n)=.

You can enter the two integers in any order.

### gcd, lcm and product

Let m, n be two positive integers such that

=, =.

What is  ?

### gcd, lcm and sum

Find two positive integers m and n, such that:

gcd(m,n) = , lcm(m,n) = , m + n = .

You can enter the two integers in any order.

### gcd and multiple

Let , be two non-zero integers. What is the condition for

pgcd(, ) pgcd(,) ?

### gcd and product

Find two positive integers m and n, such that:

gcd(m,n) = , mn = .

You can enter the two integers in any order.

### gcd and sum

Find two positive integers m and n, such that:

gcd(m,n) = , m + n = .

You can enter the two integers in any order.

### gcd, sum and product

Find two positive integers m and n, such that:

gcd(m,n) = , m + n = , mn= .

You can enter the two integers in any order.

Compute lcm(,).

Compute lcm(,,).

### lcm and product

Find two positive integers m and n, such that:

lcm(m,n) = , mn = .

You can enter the two integers in any order.

### lcm and sum

Find two positive integers m and n, such that:

lcm(m,n) = , m + n = .

You can enter the two integers in any order.

### lcm, sum and product

Find two positive integers m and n, such that:

lcm(m,n) = , m + n = , mn= .

You can enter the two integers in any order.

Other exercises on: gcd lcm   Integers   arithmetics

The most recent version

This page is not in its usual appearance because WIMS is unable to recognize your web browser.

In order to access WIMS services, you need a browser supporting forms. In order to test the browser you are using, please type the word wims here: and press Enter''.

Please take note that WIMS pages are interactively generated; they are not ordinary HTML files. They must be used interactively ONLINE. It is useless for you to gather them through a robot program.

Description: collection of exercises on gcd and lcm of integers. interactive exercises, online calculators and plotters, mathematical recreation and games

Keywords: interactive mathematics, interactive math, server side interactivity, algebra, arithmetic, number theory, prime, factorization, integer, gcd, lcm, bezout