Least Common Multiple (LCM) of 12 and 80
The least common multiple (LCM) of 12 and 80 is 240.
What is the Least Common Multiple (LCM)?
The LCM of two integers is the smallest positive integer that is divisible by both numbers. It is often used to find common denominators and solve problems involving periodic events.
Formula for LCM
The LCM of two numbers can be calculated using their GCD:
LCM(a, b) = |a × b| ÷ GCD(a, b)
How to Calculate the LCM of 12 and 80?
First, calculate the GCD of 12 and 80 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 12 ÷ 80 = 0 remainder 12 |
| 2 | 80 ÷ 12 = 6 remainder 8 |
| 3 | 12 ÷ 8 = 1 remainder 4 |
| 4 | 8 ÷ 4 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 152 and 78 | 5928 |
| 68 and 175 | 11900 |
| 200 and 140 | 1400 |
| 163 and 106 | 17278 |
| 158 and 14 | 1106 |