Step by step
The question
Question: find the least common multiple of 9 and 12.
LCM(9, 12) = ?
The multiples of 9 are 9 times 1, 2, 3 and so on.
The least common multiple, the LCM, is the smallest number in both lists.
multiples of 9: 9, 18, 27, ...
LCM: the smallest common one
1 Count up
We count up in 9s: 9, 18, 27 and 36.
In 9s: = 9, 18, 27, 36
Now in 12s: 12, 24 and 36.
In 12s: = 12, 24, 36
We count up in 9s and in 12s.
36 is the first number in both lists.
So the LCM is 36.
LCM(9, 12) = 36
Careful: every number goes into the LCM.
So it is never smaller than the biggest one.
Careful: LCM ≥ the biggest number
2 Check
Let's check: each number goes into 36.
36 ÷ 9 = 4
36 ÷ 12 = 3
No numbers are left over.
So 36 is right!
Let's look back.
First: count up.
Last: check.
Answer
LCM(9, 12) = 36