Find the LCM of several numbers, with the prime factorization behind it.
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.
LCM via GCF
lcm(a, b) = |a × b| / gcd(a, b)
LCM of a list (folding)
lcm(a, b, c) = lcm(lcm(a, b), c)
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.
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.
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.