How do you find the lowest common multiple between two numbers quickly — and how can you check that your answer is correct?
The lowest common multiple (LCM) of two numbers is the smallest number that both divide into evenly.
For the numbers 8 and 12, the LCM is 24.
Let’s look at the most efficient way to find it.
Step-by-Step Method To Find LCM
The most effective method is to use multiples of the larger number and test whether the smaller number divides into them evenly.
Example: LCM of 8 and 12
- $12 \div 8$ → remainder → ❌
- $12 \times 2 = 24$, $24 \div 8 = 3$ → ✅
So, the LCM of 8 and 12 is 24.
How To Check Your Answer
Multiply both numbers together to find a common multiple, then work backwards to find the lowest.
- $8 \times 12 = 96$
Now check smaller multiples of 12:
- $12 \times 7 = 84$, $84 \div 8$ → remainder
- $12 \times 6 = 72$, $72 \div 8 = 9$ → ✅
- $12 \times 5 = 60$, $60 \div 8$ → remainder
- $12 \times 4 = 48$, $48 \div 8 = 6$ → ✅
- $12 \times 3 = 36$, $36 \div 8$ → remainder
- $12 \times 2 = 24$, $24 \div 8 = 3$ → ✅
- $12 \times 1 = 12$, $12 \div 8$ → remainder
You now have common multiples: (96, 72, 48, 24)
The smallest is 24, confirming the lowest common multiple.
Summary
The lowest common multiple of 8 and 12 is 24.
To find the LCM:
- Multiply the larger number by 1, 2, 3… until the smaller number divides into one of the results.
- Or, check backwards from the full product.
This method is especially useful for solving fraction problems, where finding a shared denominator is essential.