#
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*= ?

### Find gcd

Compute gcd(,).

### Find gcd-3

Compute gcd(,,).

### Find gcd II

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.

### Find lcm

Compute lcm(,).

### Find lcm-3

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

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- 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