LCM Calculator (Least Common Multiple)

Factor each number into primes, take every prime to the highest power it has in any of the numbers, and multiply. For 20 = 2² · 5 and 30 = 2 · 3 · 5, that is 2² · 3 · 5 = 60. For two numbers you can also divide their product by the GCF: 20 · 30 / 10 = 60. Or list multiples until the first match.

It is 72. In primes, 24 = 2³ · 3 and 36 = 2² · 3², so the LCM is 2³ · 3² = 72. The GCF is 2² · 3 = 12, and the check works: 24 · 36 / 12 = 864 / 12 = 72. The multiples of 24 are 24, 48, 72, and 72 is also a multiple of 36.

It is 24. The multiples of 8 are 8, 16, 24 and the multiples of 12 are 12, 24, so 24 is the first one they share. With primes, 8 = 2³ and 12 = 2² · 3 give 2³ · 3 = 24. The GCF of 8 and 12 is 4, and 8 · 12 / 4 = 24.

It is 4. Since 2 divides 4 evenly, 4 is already a multiple of both numbers, and nothing smaller is a multiple of 4. This holds whenever one number divides the other: the LCM is the larger number.

The LCM, also called the lowest or least common multiple, is the smallest positive whole number that is a multiple of every number in a set. For 4 and 6 it is 12. It always exists for positive whole numbers and is never smaller than the largest number in the set.

It finds the smallest number that all of your numbers divide evenly. This one also shows the greatest common factor, the prime factorization of every number, and the steps that lead to the answer, so you can follow along or check homework.

The LCM is the smallest number that all the numbers divide, so it is at least as large as the largest of them. The GCD, also called the GCF, is the largest number that divides all of them, so it is at most the smallest. For 12 and 18 the LCM is 36 and the GCD is 6.

For two numbers, the product of the LCM and the GCF equals the product of the numbers: LCM × GCF = a × b. For 12 and 18, 36 × 6 = 216 = 12 × 18. That gives a shortcut, LCM = a × b / GCF. It works for two numbers only; with three or more you combine them two at a time.

Yes. This one takes two to five numbers. It takes each prime to its highest power across all of them, which is the same as finding LCM(LCM(a, b), c) and so on. For 4, 6 and 10 the answer is 2² · 3 · 5 = 60.

It finds common denominators for adding fractions, and it tells you when repeating events line up again. Two buses that leave every 12 and every 18 minutes depart together every 36 minutes. It also sizes packages so nothing is left over: hot dogs sold in 10s and buns in 8s match up at 40 of each.

It is the key step in adding and subtracting fractions with different denominators, since the LCM gives the smallest common denominator. It also solves scheduling and cycle problems, such as when gears with different tooth counts return to their starting positions together.

The least common denominator (LCD) of fractions is the LCM of their denominators. For 1/4 and 1/6 the LCD is 12, so they become 3/12 and 2/12. Enter the denominators here, and use the fraction calculator to add or subtract the fractions.

It is their product. Two numbers are relatively prime when their GCF is 1, and then LCM = a · b / 1. The LCM of 3 and 5 is 15, and the LCM of 8 and 9 is 72, even though 8 and 9 are not prime numbers themselves.

The LCM is defined for positive whole numbers here, and every common multiple of a set that includes 0 is 0, which is not useful. Enter whole numbers from 1 to 1,000,000. For a negative number, use its positive value: the LCM of -4 and 6 is the LCM of 4 and 6, which is 12.