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 can divide into with no remainder.
For the numbers 4 and 6, the LCM is 12.
Let’s walk through the most efficient method to find it.
Step-by-Step Method To Find LCM
To find the LCM between two numbers, follow this approach:
- Start with the larger number.
- Check: can the smaller number divide evenly into it?
- If not, multiply the larger number by 2, 3, 4, etc., and check each time until the smaller number divides in cleanly.
Example: Find the LCM of 4 and 6
- $6 \div 4 = 1$ remainder → ❌
- $6 \times 2 = 12$, and $12 \div 4 = 3$ → ✅
Therefore, the LCM of 4 and 6 is 12.
How To Check Your Answer
To confirm your answer, you can multiply both numbers together and work backwards to find the lowest valid common multiple.
- $4 \times 6 = 24$ (a common multiple, not necessarily the lowest)
Now count down:
- $6 \times 3 = 18$, $18 \div 4 = 4.5$ → ❌
- $6 \times 2 = 12$, $12 \div 4 = 3$ → ✅
- $6 \times 1 = 6$, $6 \div 4 = 1.5$ → ❌
Your smallest value that both divide into is 12. That confirms the LCM.
Summary
The lowest common multiple of 4 and 6 is 12.
To find it:
- Multiply the larger number by 1, 2, 3… until the smaller number divides in evenly.
- Use this method to confidently work with problems involving fractions, where a common denominator is needed.