Step by step
The question
Question: find the least common multiple of 4 and 10.
LCM(4, 10) = ?
The multiples of 4 are 4 times 1, 2, 3 and so on.
The least common multiple, the LCM, is the smallest number in both lists.
multiples of 4: 4, 8, 12, ...
LCM: the smallest common one
1 Count up
We count up in 4s: 4, 8, 12, 16 and 20.
In 4s: = 4, 8, 12, 16, 20
Now in 10s: 10 and 20.
In 10s: = 10, 20
We count up in 4s and in 10s.
20 is the first number in both lists.
So the LCM is 20.
LCM(4, 10) = 20
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 20.
20 ÷ 4 = 5
20 ÷ 10 = 2
No numbers are left over.
So 20 is right!
Let's look back.
First: count up.
Last: check.
Answer
LCM(4, 10) = 20