Least Common Multiple (LCM) of 132 and 82
The least common multiple (LCM) of 132 and 82 is 5412.
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 132 and 82?
First, calculate the GCD of 132 and 82 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 132 ÷ 82 = 1 remainder 50 |
| 2 | 82 ÷ 50 = 1 remainder 32 |
| 3 | 50 ÷ 32 = 1 remainder 18 |
| 4 | 32 ÷ 18 = 1 remainder 14 |
| 5 | 18 ÷ 14 = 1 remainder 4 |
| 6 | 14 ÷ 4 = 3 remainder 2 |
| 7 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 85 and 73 | 6205 |
| 132 and 119 | 15708 |
| 119 and 190 | 22610 |
| 167 and 197 | 32899 |
| 145 and 10 | 290 |