What is the general formula for computing the least common multiple of two positive integers using their greatest common divisor?

Conditions

• a and b are positive integers.

Reasoning, step by step

1. Identify the two positive integers a and b.
2. Compute their greatest common divisor, GCD(a,b).
3. Multiply a and b together.
4. Divide the product by the GCD to get the LCM.

Example

The video writes 'LCM = $a\cdot b$ / GCD' and applies it to 4 and 6: gcd(4,6)=2, so LCM(4,6) = ($4*6$)/2 = $24/2 = 12$.

Common misconceptions

• Forgetting to divide by the GCD, which would incorrectly yield the product instead of the LCM for non-coprime numbers.
• Confusing the GCD formula with the coprime product shortcut.

Watch the explanation

Explore next

• When can you skip the GCD calculation and just multiply the numbers?
• How does the remainder sequence trick help in solving CRT?
• What is the time complexity of the iterative CRT method?