LCM and HCF

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Simon Thomas

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Simon Thomas 5 years, 1 month ago

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Simon Thomas 5 years, 1 month ago

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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

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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	[ 1, 1, 1, 3 ]
y_powers	list	[ 0, 1, 2, 2 ]
z_powers	list	[ 4, 1, 0, 2 ]
x	number	10290
y	number	3675
z	number	2352
hcf_xy	number	735
hcf_xz	number	294
lcm_xy	number	51450
lcm_xz	number	82320
hcf_xyz	decimal	dec("147")
lcm_xyz	decimal	dec("411600")
primes	list	List of 15 items

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Name

Data type

Value

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

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Description

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Generated value: `list`

[ 1, 1, 1, 3 ]

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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 $(x,y,z) = \var{show_factors(lcm_xyz)}=\var{lcm_xyz}$

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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

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Simon Thomas 5 years, 1 month ago

Simon Thomas 5 years, 1 month ago

Error in variable testing condition

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Generated value: `list`

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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, 1 month ago

Simon Thomas 5 years, 1 month ago

Error in variable testing condition

Error

Warning

Generated value: list

Parts

Number entry

Advanced settings

Generated value: `list`