Least Common Multiple Calculator
Find the LCM of several numbers via GCD — the key to adding fractions and scheduling problems.
Inputs
Least Common Multiple (LCM)
12
Input Numbers
4, 6
Step by step
Inputs
= 4, 6
GCF(4, 6)
= 2
LCM(4, 6)
(4 / 2) × 6 = 2 × 6
= 12
Verification
12 ÷ 4 = 3 (integer), 12 ÷ 6 = 2 (integer)
How it works
The Least Common Multiple of a set of numbers is the smallest positive integer that is a multiple of every number in the set. It's calculated as lcm(a, b) = (a × b) / gcd(a, b), where gcd is the Greatest Common Factor. For a list, fold pairwise: lcm(a, b, c) = lcm(lcm(a, b), c). The LCM is the key to finding a common denominator when adding fractions.
Formulas
LCM via GCF
lcm(a, b) = |a × b| / gcd(a, b)
- a
- First number
- b
- Second number
LCM of a list (folding)
lcm(a, b, c) = lcm(lcm(a, b), c)
Frequently Asked Questions
What is the LCM of 4 and 6?
gcd(4, 6) = 2. LCM = 4 × 6 / 2 = 24 / 2 = 12. Verify: 12 ÷ 4 = 3 ✓ and 12 ÷ 6 = 2 ✓. The LCM of 4 and 6 is 12.
What is the LCM used for in fractions?
To add or subtract fractions with different denominators, you need a common denominator. The Least Common Denominator (LCD) is the LCM of the denominators. For ½ + ⅓: LCD = lcm(2, 3) = 6, giving 3/6 + 2/6 = 5/6.
Is LCM(a, b) × GCF(a, b) = a × b always true?
Yes, for positive integers: lcm(a, b) × gcd(a, b) = a × b. This identity is the basis of the efficient calculation. For example, lcm(4, 6) × gcd(4, 6) = 12 × 2 = 24 = 4 × 6.