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 3 and 5, the LCM is 15.
Let’s explore the most efficient method to arrive at that answer.
Step-by-Step Method To Find LCM
To find the LCM between two numbers, follow these steps:
- 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.
This is the most efficient method.
Example: Find the LCM of 3 and 5
- $5 \div 3 = 1$ remainder → ❌
- $5 \times 2 = 10$, and $10 \div 3 = 3$ remainder → ❌
- $5 \times 3 = 15$, and $15 \div 3 = 5$ → ✅
Therefore, the LCM of 3 and 5 is 15.
How To Check Your Answer
A quick way to check is to multiply both numbers together and then work backwards to confirm that no smaller value is valid.
- $3 \times 5 = 15$
Try smaller multiples of 5:
- $5 \times 2 = 10$, $10 \div 3 = 3.33$ → ❌
- $5 \times 1 = 5$, $5 \div 3 = 1.66$ → ❌
Only $15$ is divisible by both 3 and 5, confirming it is the lowest common multiple.
Summary
The lowest common multiple of 3 and 5 is 15.
To find it quickly:
- Start with the larger number.
- Multiply it by 1, 2, 3… and check if the smaller number divides evenly.
- The first match is your LCM.
This strategy is especially useful when working with fractions, where finding a common denominator is required.