Find the least common multiple of 4 and 6.

How we read your problem

Find the least common multiple of the numbers.

Step-by-step solution

1. 1

   Prime factorization of each number

   $$4 = 2^{2},\quad 6 = 2 \times 3$$
2. 2

   Use the GCF to combine 4 and 6

   $$\operatorname{lcm}(4, 6) = \frac{4 \times 6}{\gcd(4, 6)} = \frac{24}{2} = 12$$
3. 3

   Confirm with prime factors

   Take every prime that appears, each with its largest exponent.

   $$2^{2} \times 3 = 12$$

Formulas used

• LCM from GCF

  $$\operatorname{lcm}(a, b) = \frac{|a \cdot b|}{\gcd(a, b)}$$

12 is the smallest positive number that every input divides exactly.

Verification

• 12 ÷ 4 = 3
• 12 ÷ 6 = 2