How to find the least common multiple
- Type two or more whole numbers, separated by commas or spaces.
- The LCM appears first, with the GCF and each number's prime factorization.
Methods
Prime factors: take every prime that appears in any of the numbers, at its highest power, and multiply. 4 = 2², 6 = 2 × 3, 10 = 2 × 5, so LCM = 2² × 3 × 5 = 60. Using the GCF: for two numbers, LCM(a, b) = a × b ÷ GCF(a, b). LCM(12, 18) = 216 ÷ 6 = 36. For more numbers, apply it one pair at a time, which is what this calculator does with exact big-integer arithmetic so even huge results are correct.
The LCM is the lowest common denominator when adding fractions: 1/4 + 1/6 + 1/10 uses 60 as the denominator. It also answers timing problems: if one bus comes every 12 minutes and another every 18, they arrive together every 36 minutes. Gear teeth, repeating schedules and musical rhythms follow the same idea.
FAQ
What is the LCM of 4 and 6?
12.
How is LCM different from GCF?
LCM is the smallest number all of yours divide into; GCF is the largest number that divides all of yours.
What is the LCM of two coprime numbers?
Their product, because they share no prime factors. LCM(8, 15) = 120.