# 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

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