Least Common Multiple (LCM) of 80 and 132
The least common multiple (LCM) of 80 and 132 is 2640.
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 80 and 132?
First, calculate the GCD of 80 and 132 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 80 ÷ 132 = 0 remainder 80 |
| 2 | 132 ÷ 80 = 1 remainder 52 |
| 3 | 80 ÷ 52 = 1 remainder 28 |
| 4 | 52 ÷ 28 = 1 remainder 24 |
| 5 | 28 ÷ 24 = 1 remainder 4 |
| 6 | 24 ÷ 4 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 65 and 68 | 4420 |
| 164 and 142 | 11644 |
| 28 and 194 | 2716 |
| 157 and 122 | 19154 |
| 180 and 171 | 3420 |