LCM Calculator
Lowest Common Multiple ⚡
Find the Lowest Common Multiple (LCM) — also called the Least Common Multiple — of two or more numbers instantly, with full working shown.
Find the Lowest Common Multiple (LCM) — also called the Least Common Multiple — of two or more numbers instantly, with full working shown.
The Lowest Common Multiple (LCM) — also called the Least Common Multiple — is the smallest positive integer that is exactly divisible by two or more given numbers. For example, LCM(4, 6) = 12, because 12 is the smallest number that both 4 and 6 divide into without a remainder.
The first few multiples of 4 are: 4, 8, 12, 16, 20... The first few multiples of 6 are: 6, 12, 18, 24... The smallest number in both lists is 12.
The most efficient method uses the relationship between LCM and GCD:
LCM(a, b) = (a × b) ÷ GCD(a, b)
For example: LCM(12, 15) — GCD(12, 15) = 3, so LCM = (12 × 15) ÷ 3 = 180 ÷ 3 = 60.
An alternative method uses prime factorisation: find the prime factors of each number, then take each prime factor at its highest power. For LCM(12, 15): 12 = 2² × 3, 15 = 3 × 5. Taking the highest powers: 2² × 3 × 5 = 60.
What is the LCM of any number and 1?
The number itself. LCM(n, 1) = n, since n is the smallest number divisible by both n and 1.
Can the LCM be smaller than the largest input?
No. The LCM is always greater than or equal to the largest of the input numbers, because it must be divisible by all inputs.
What is the relationship between LCM and GCD?
For any two positive integers a and b: LCM(a, b) × GCD(a, b) = a × b. This means if you know the GCD, you can always find the LCM instantly, and vice versa.
What is the LCM of two prime numbers?
The LCM of two different prime numbers is always their product. For example, LCM(5, 7) = 35 — because two primes share no common factors, so GCD = 1 and LCM = (5 × 7) ÷ 1 = 35.
What is the difference between LCM and HCF?
LCM finds the smallest number both inputs divide into. HCF (or GCD) finds the largest number that divides into both inputs. They are related — LCM × HCF = the product of the two numbers.