LCM and HCF

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Simon Thomas

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Simon Thomas 5 years, 2 months ago

Published this.

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Simon Thomas 5 years, 2 months ago

Created this.

Name	Status	Author	Last Modified
LCM and HCF	draft	Simon Thomas	16/03/2020 13:42
Prime Factorisation	draft	Simon Thomas	16/03/2020 13:42
NB4 - HCF	Ready to use	Andrew Neate	10/04/2024 09:14
NB5 - LCM	Ready to use	Andrew Neate	10/04/2024 09:15
NG1 Simplify (cancel down) Fractions	Ready to use	Andrew Neate	10/04/2024 09:35
Merryn's copy of LCM and HCF	Ready to use	Merryn Horrocks	07/03/2024 01:07

There are 11 other versions that do you not have access to.

Question statement

$x = \var{x}$

$y = \var{y}$

$z = \var{z}$

By considering the prime factorisation of $x, y$ and $z$ , or otherwise, find:

Give any introductory information the student needs.

			Name	Type	Generated Value

x_powers	list	[ 4, 1, 0, 2 ]
y_powers	list	[ 0, 4, 0, 1 ]
z_powers	list	[ 4, 1, 0, 1 ]
x	number	2352
y	number	567
z	number	336
hcf_xy	number	21
hcf_xz	number	336
lcm_xy	number	63504
lcm_xz	number	2352
hcf_xyz	decimal	dec("21")
lcm_xyz	decimal	dec("63504")
primes	list	List of 15 items

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
[random(1..4),random(0..4),random(0..3),random(0..3)]

JME function reference

Description

Describe what this variable represents, and list any assumptions made about its value.

Can an exam override the value of this variable?

Generated value: `list`

[ 4, 1, 0, 2 ]

→ Used by:

hcf_xy
hcf_xyz
hcf_xz
lcm_xy
lcm_xyz
lcm_xz
x

This variable doesn't seem to be used anywhere.

Advice

We can write $x,y,z$ as a product of prime factors as follows:

$x=\var{x}=\var{show_factors(x)}$

$y=\var{y}=\var{show_factors(y)}$

$z=\var{z}=\var{show_factors(z)}$

For HCF of $\var{x}$ and $\var{y}$ we need to multiply each factor the least number of times it occurs in either $\var{x}$ or $\var{y}$

i.e. HCF $(x,y) = \var{show_factors(hcf_xy)}=\var{hcf_xy}$

For LCM of $\var{x}$ and $\var{y}$ we need to multiply each factor the greatest number of times it occurs in either $\var{x}$ or $\var{y}$

i.e. LCM $(x,y) = \var{show_factors(lcm_xy)}=\var{lcm_xy}$

For HCF of $\var{x}$ and $\var{z}$ we need to multiply each factor the least number of times it occurs in either $\var{x}$ or $\var{z}$

i.e. HCF $(x,z) = \var{show_factors(hcf_xz)}=\var{hcf_xz}$

For LCM of $\var{x}$ and $\var{z}$ we need to multiply each factor the greatest number of times it occurs in either $\var{x}$ or $\var{z}$

i.e. LCM $(x,z) = \var{show_factors(lcm_xz)}=\var{lcm_xz}$

For HCF of $\var{x},\var{y}$ and $\var{z}$ we need to multiply each factor the least number of times it occurs in either $\var{x}$ or $\var{y}$ or $\var{z}$

i.e. HCF $(x,y,z) = \var{show_factors(hcf_xyz)}=\var{hcf_xyz}$

For LCM of $\var{x},\var{y}$ and $\var{z}$ we need to multiply each factor the greatest number of times it occurs in either $\var{x}$ or $\var{y}$ or $\var{z}$

i.e. LCM $(x,y,z) = \var{show_factors(lcm_xyz)}=\var{lcm_xyz}$

Give a worked solution to the whole question.

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This question is used in the following exams:

Working with Prime Factorisation by Simon Thomas in Maths support.
Laura MATH1901 by Blathnaid Sheridan in Blathnaid's workspace.
MATH1901 (Laura's Group) by Laura Cooke in Laura's workspace.
Prime Factorisation by Chris Templet in Chris's workspace.
MATH1901 (Paul&Laura) by Blathnaid Sheridan in Blathnaid's workspace.
MATH1901 Continuous Assessment by Paul Molloy in Paul's workspace.

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Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

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Checkpoint description

Simon Thomas 5 years, 2 months ago

Simon Thomas 5 years, 2 months ago

Error in variable testing condition

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Generated value: `list`

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Number entry

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LCM and HCF

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

Simon Thomas 5 years, 2 months ago

Simon Thomas 5 years, 2 months ago

Error in variable testing condition

Error

Warning

Generated value: list

Parts

Number entry

Advanced settings

Generated value: `list`