FractionReference

Least common multiple

The smallest number they all divide into — which is the common denominator you need to add fractions. Type two or more whole numbers, separated by commas or spaces.

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Common questions

What is the least common multiple?
The smallest whole number that every one of your numbers divides into evenly. For 4 and 6 it is 12: both divide 12, and nothing smaller works.
How do I find the LCM by hand?
Factor each number into primes, then take the highest power of each prime that appears anywhere and multiply. 4 is 2² and 6 is 2 × 3, so the LCM is 2² × 3 = 12. The shared-factor table on this page shows it.
What is the LCM used for?
Adding and subtracting fractions. To add 1/4 and 1/6 you need a common denominator, and the LCM of 4 and 6 is 12 — so the sum becomes 3/12 plus 2/12, which is 5/12.
Is the LCM always the two numbers multiplied together?
Only when they share no factors. 4 × 6 is 24, which every multiple test passes, but 12 is smaller and works too. The product is a common multiple; the LCM is the least one, and they differ by exactly the GCF.

Related

Greatest common factorThe other half: the largest number that divides them all. Add fractionsThe LCM, applied — the common denominator found for you. Equivalent fractions chartRewriting over a new denominator, printable.
Where this comes from. Exact rational arithmetic on the values shown — fractions are pairs of integers until display, and inch–metric conversion uses 25.4 mm to the inch, exact by definition since 1959. Factorisation is by trial division, exact for every number this tool accepts. See the full methodology.