Enter two or more whole numbers to find their least common multiple, with the steps shown.
The least common multiple of some whole numbers is the smallest positive number that every one of them divides into evenly. The LCM of 4 and 6 is 12, because 12 is the first number that appears in both the list of multiples of 4, which is 4, 8, 12, and the list of multiples of 6, which is 6, 12. It is written LCM(4, 6) = 12. You need it to add fractions with different denominators and to find when repeating events line up.
Break each number into primes, then multiply the highest power of every prime that appears in any of them. For 12, 18 and 24, the factorizations are 2 × 2 × 3, 2 × 3 × 3 and 2 × 2 × 2 × 3. The highest power of 2 is 2³ and of 3 is 3², so the LCM is 8 × 9, which is 72. The calculator shows these factorizations and the combined product.
For two numbers, the LCM is their product divided by their greatest common divisor, or GCD: LCM(a, b) = a × b ÷ GCD(a, b). For 100 and 75 the GCD is 25, so the LCM is 7,500 ÷ 25, which is 300. For more than two numbers, find the LCM of the first two, then the LCM of that result with the third, and so on. Very large numbers use only this method, since breaking them into primes would take too long.
List the multiples of each number and pick the smallest one they share, or divide their product by their greatest common divisor. The LCM of 4 and 6 is 12.
Find the LCM of the first two, then find the LCM of that answer and the third number. The prime factorization method does it in one step.
It is the larger number. For example, the LCM of 6 and 18 is 18.
It is their product, because primes share no factors. The LCM of 17 and 19 is 323.
For two numbers, the LCM times the GCD equals the product of the two numbers.
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