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HCF and LCM by Listing
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Foundational skills
Find common elements in two lists
\[ \text{Lists A \& B} \rightarrow \text{overlap} \]
Identify numbers in two given lists.
Identify the smallest number in a list
\[ 12, 8, 24, 6 \rightarrow 6 \]
Find the minimum value in a list.
Identify the largest number in a list
\[ 1, 2, 4, 6, 12 \rightarrow 12 \]
Find the maximum value in a list.
Common multiples
Find common multiples of two numbers
\[ 4, 6 \rightarrow 12, 24, 36… \]
List first few common multiples.
Find common multiples of three numbers
\[ 2, 3, 5 \rightarrow 30, 60… \]
Common multiples of three numbers.
Find the LCM of two numbers
\[ \text{LCM}(6, 8) = 24 \]
Find the lowest common multiple.
Find the LCM of three numbers
\[ \text{LCM}(3, 4, 6) = 12 \]
LCM of three numbers by listing.
Common factors
Find common factors of two numbers
\[ 18, 24 \rightarrow 1, 2, 3, 6 \]
List all shared factors.
Find common factors of three numbers
\[ 12, 18, 24 \rightarrow 1, 2, 3, 6 \]
Factors common to all three.
Find the HCF of two numbers
\[ \text{HCF}(24, 36) = 12 \]
Find the highest common factor.
Find the HCF of three numbers
\[ \text{HCF}(12, 18, 30) = 6 \]
HCF of three numbers by listing.
LCM in context
LCM context: Events happening together
\[ \text{Buses} \rightarrow \text{next together?} \]
When two cycles align.
LCM context: Buying equal quantities
\[ \text{Packs of 6 \& 8} \rightarrow ? \]
Equal amounts from different packs.
LCM context: Tiling or fitting
\[ 4\text{cm}, 6\text{cm} \rightarrow 12\text{cm} \]
Length divisible by both sizes.
LCM context: Cycle alignment
\[ \text{Every 3 \& 5 days} \rightarrow ? \]
When recurring events coincide.
HCF in context
HCF context: Largest equal groups
\[ 24, 36 \rightarrow 12 \text{ groups} \]
Maximum identical groups.
HCF context: Cutting into equal pieces
\[ 48\text{m}, 60\text{m} \rightarrow 12\text{m} \]
Longest equal piece length.
HCF context: Sharing fairly
\[ 18, 24 \rightarrow \text{max bags?} \]
Maximum identical sets.
HCF context: Tiling a rectangle
\[ 24 \times 36 \rightarrow 12\text{m tile} \]
Largest square tile size.
Verifying and interpreting
Verify a given HCF
\[ \text{HCF}(18, 30) = 6 \text{ ?} \]
Check if HCF is correct.
Verify a given LCM
\[ \text{LCM}(8, 12) = 48 \text{ ?} \]
Check if LCM is correct.
Use HCF and LCM relationship
\[ \text{HCF} \times \text{LCM} = a \times b \]
Find missing number from HCF/LCM.
Choosing HCF or LCM
Identify whether HCF or LCM needed
\[ \text{Problem} \rightarrow \text{HCF or LCM?} \]
Choose correct operation.
Match problems to HCF or LCM
\[ A, B, C \rightarrow \text{which is LCM?} \]
Classify multiple scenarios.
Special cases
HCF of coprime numbers
\[ \text{HCF}(8, 15) = 1 \]
Numbers with no common factors.
LCM when one is multiple of other
\[ \text{LCM}(6, 24) = 24 \]
LCM is the larger number.
HCF when one is factor of other
\[ \text{HCF}(8, 32) = 8 \]
HCF is the smaller number.
HCF and LCM of the same pair
\[ 12, 20 \rightarrow \text{both} \]
Find both HCF and LCM.
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