Least Common Multiple (LCM)
Practise finding the least common multiple of two numbers — the key to adding fractions with unlike denominators.
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How to find the LCM
The least common multiple of two numbers is the smallest number both divide into. It’s exactly what you need when adding fractions with different denominators.
- List the multiples of each number (its times table).
- Find the first one they have in common.
- That’s the LCM.
A shortcut: LCM = the two numbers multiplied, then divided by their GCF.
Worked examples
Tips & common mistakes
Listing multiples works well for small numbers; the GCF shortcut (multiply, then divide by the GCF) is faster for bigger ones. Type the LCM.
- Just multiplying the two numbers — that’s a common multiple, but not always the least (4 and 6 give 24, not the correct 12).
- Picking a shared multiple that isn’t the smallest.
- Confusing LCM (a multiple, so bigger) with GCF (a factor, so smaller).
Frequently asked questions
What is the least common multiple?
The smallest number that both numbers divide into. The LCM of 4 and 6 is 12.
How do I find the LCM?
List the multiples of each number and take the first they share, or multiply the two numbers and divide by their GCF.
What is the LCM used for?
Adding and subtracting fractions with unlike denominators — the LCM gives the least common denominator.
Isn’t the LCM just the two numbers multiplied?
Not always. That gives a common multiple, but the least one is that product divided by the GCF. For 4 and 6 it’s 12, not 24.
How is LCM different from GCF?
LCM is the smallest shared multiple (bigger than the numbers); GCF is the largest shared factor (smaller than them).