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Details for problem "Determine gcd and lcm by comparing multiples & divisors"

Quickname: 4978

Suitable for K-12 grades: Grade 5 Grade 6 Grade 7

Elementary School, Primary School, Junior High School, Middle School, High School.

Summary

For two given numbers, the gcd and lcm are determined by comparing lists of multiples or divisors

Examples

For two given numbers, the gcd and lcm are determined by comparing lists of multiples or divisors (Beispiel für die Lösung) For two given numbers, the gcd and lcm are determined by comparing lists of multiples or divisors (Example for this math problem)

Description

Two numbers are given. For these numbers, either the greatest common divisor (gcd) or least common multiple (lcm) have to be determined. The problem generator can be configured to ask only for one of them, or for both in a random fashion.

For this problem type, the straightforward approach to compare

- the lists of divisors for both numbers to look for the greatest number that appears in both lists to determine the greatest common divisor

- the lists of multiples for both numbers to look for the first = least number that appears in both lists to determine the least common multiple


The number range can be chosen, and the number of problems presented is selectable.

Optionally, as a hint, the first few multiples (for the lcm) or divisors (for the gcd) can be given with the problem.


Topics: Arithmetic Divisibility

Tags: Division Multiplication

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Customization options for this problem

Parameter
Possible values
Number of problems
1, 2, 3, 4, 5, 6, 7, 8, 9, 10
Ask for...
gcd and lcm, gcd, lcm
Number range of product
50, 80, 100, 200, 500, 1000
Provide first few items of lists
Yes, No
Explain lcm and gcd
Yes, No

Similar problems

Remark
Description
Name and direct link
Check for divisors and multiples of a number
Determine whether a number is a factor or multiple of another.
Find divisors of a number
For a given number, all factors have to be listed.
Application and detailed computational steps for Euclidean Algorithm
Compute the GCD step by step with the Euclidian Algorithm.
Is also available for the lcm with prime factorization approach
The lcm is to be derived for two given numbers.
Find multiples
For a given number, list the first n multiples.

dw-Math worksheet templates that do contain this problem

Name
Title
Description
Greatest Common Divisor
Two ways to determine the gcd of two numbers.


Creative Commons License
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This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.


Deutsche Version dieser Aufgabe
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