Three ways to find it
Same answer, different amount of writing. Pick the method that matches your homework instructions.
1. List the multiples
Write multiples of each number until you spot the first shared value. Fine for small numbers; miserable for 84 and 126.
Multiples of 8: 8, 16, 24, 32, 40…
Multiples of 12: 12, 24, 36… → LCM(8, 12) = 24
Multiples of 12: 12, 24, 36… → LCM(8, 12) = 24
2. Prime factorization
Factor each number. For every prime that appears, keep the highest power. Multiply those together. This is the method most textbooks want to see.
8 = 23 · 12 = 22 × 3 → keep 23 and 3 → LCM = 24
Common slip: using the lowest power instead of the highest. Lowest powers give you the GCD, not the LCM.
3. GCD shortcut
Compute GCD with Euclidean division, then LCM = a×b / GCD. Fastest for two numbers; for three or more, apply pairwise.
What LCM is not
- Not the same as the product (product is often much larger).
- Not always bigger than both numbers in a dramatic way — LCM(7,14) is just 14.
- Not defined the same way for fractions in most school courses (though a related idea exists).
Next: Formula & Methods or jump to Worked Examples.