How do you find the lowest common multiple between two numbers quickly — and how can you check your answer?
The lowest common multiple (LCM) of two numbers is the smallest number that both divide into with no remainder.
For the numbers 8 and 10, the LCM is 40.
Let’s explore the most efficient way to find it.
Step-by-Step Method To Find LCM
The most effective strategy is to use multiples of the larger number and check if the smaller number divides into any of them.
Example: LCM of 8 and 10
- $10 \div 8$ → remainder → ❌
- $10 \times 2 = 20$, $20 \div 8$ → remainder → ❌
- $10 \times 3 = 30$, $30 \div 8$ → remainder → ❌
- $10 \times 4 = 40$, $40 \div 8 = 5$ → ✅
So, the LCM of 8 and 10 is 40.
How To Check Your Answer
You can also check your answer by multiplying the two numbers and working backward.
- $8 \times 10 = 80$
Now count down:
- $10 \times 7 = 70$, $70 \div 8$ → remainder
- $10 \times 6 = 60$, $60 \div 8$ → remainder
- $10 \times 5 = 50$, $50 \div 8$ → remainder
- $10 \times 4 = 40$, $40 \div 8 = 5$ → ✅
- $10 \times 3 = 30$, $30 \div 8$ → remainder
- $10 \times 2 = 20$, $20 \div 8$ → remainder
- $10 \times 1 = 10$, $10 \div 8$ → remainder
You now have common multiples: (80, 40)
The smallest one is 40, confirming it as the lowest common multiple.
Summary
The lowest common multiple of 8 and 10 is 40.
To find the LCM:
- Multiply the larger number by 1, 2, 3… until the smaller number divides in evenly.
- You can also confirm by working backward from their product.
Knowing how to find the LCM is especially helpful when adding or subtracting fractions with different denominators.