How it is calculated
GCD by Euclid’s algorithm: gcd(a, b) = gcd(b, a mod b) until the remainder is zero.
For several numbers, apply the operation in turn.
Worked example
84 and 120: 120 = 84 × 1 + 36, 84 = 36 × 2 + 12, 36 = 12 × 3 + 0, so gcd = 12 and lcm = 84 × 120 ÷ 12 = 840.
Frequently asked questions
When do I use the LCM?
To find a common denominator, or when two repeating events coincide.
And the GCD?
To simplify fractions or split things into the largest equal groups.
What are coprime numbers?
Numbers whose GCD is 1, such as 8 and 15.