HCF & LCM Flashcards

All 6 cards in this deck

What is the highest common factor (HCF) of two numbers?

The largest number that is a factor of both of them.
e.g. HCF of 60 and 84 is 12

What is the lowest common multiple (LCM) of two numbers?

The smallest number that is a multiple of both of them.
e.g. LCM of 24 and 40 is 120

How do you find the HCF from prime factorisations in index form?
e.g. $A = 2^3 \times 3 \times 5$, $B = 2^2 \times 3 \times 5^2$

Multiply the lowest power of each prime that appears in both.
HCF $= 2^2 \times 3 \times 5 = 60$

How do you find the LCM from prime factorisations in index form?
e.g. $A = 2^3 \times 3 \times 5$, $B = 2^2 \times 3 \times 5^2$

Multiply the highest power of every prime that appears in either.
LCM $= 2^3 \times 3 \times 5^2 = 600$

In a word problem, when do you need the LCM and when do you need the HCF?

LCM for repeating events happening together or a smallest possible total; HCF for splitting into the largest equal groups or largest identical tiles.

True or false? The LCM of two numbers is always the two numbers multiplied together.

False. HCF $\times$ LCM $=$ product of the two numbers, so this only happens when the HCF is 1.