Factors, multiples, HCF and LCM

Finding factors and multiples, the highest common factor (HCF) and the lowest common multiple (LCM) of two numbers.

Factors and multiples

A factor divides a number exactly. A multiple is the number times $1, 2, 3, \ldots$

Factors of $18$: $1, 2, 3, 6, 9, 18$. Multiples of $6$: $6, 12, 18, 24, \ldots$

Example 1●

Find the HCF and LCM of $12$ and $18$.

Factors of $12$: $1, 2, 3, 4, 6, 12$. Factors of $18$: $1, 2, 3, 6, 9, 18$. HCF $= 6$.

Multiples of $18$: $18, 36, \ldots$ The first that $12$ divides is $36$. LCM $= 36$.

Example 2●●

Two lights flash every $8$ s and every $10$ s. They flash together now. When do they next flash together?

This is the LCM of $8$ and $10$: multiples of $10$ are $10, 20, 30, 40$, and $8$ divides $40$.

After $40$ seconds.

Flashcards

Factor

A number that divides exactly into another.

HCF of 12 and 18

$6$

LCM of 4 and 6

$12$

Practice

Find the HCF of $12$ and $18$.
Find the LCM of $12$ and $18$.
Lights flash every $8$ s and $10$ s. After how many seconds do they next flash together?
How many factors does $12$ have?
Which is not a factor of $36$?
Find the HCF of $28$ and $42$.
Find the LCM of $6$ and $10$.
What is the smallest 3-digit multiple of $7$?