Least Common Multiple (LCM) of 132 and 171
The least common multiple (LCM) of 132 and 171 is 7524.
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 171?
First, calculate the GCD of 132 and 171 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 132 ÷ 171 = 0 remainder 132 |
| 2 | 171 ÷ 132 = 1 remainder 39 |
| 3 | 132 ÷ 39 = 3 remainder 15 |
| 4 | 39 ÷ 15 = 2 remainder 9 |
| 5 | 15 ÷ 9 = 1 remainder 6 |
| 6 | 9 ÷ 6 = 1 remainder 3 |
| 7 | 6 ÷ 3 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 31 and 84 | 2604 |
| 60 and 82 | 2460 |
| 20 and 80 | 80 |
| 117 and 137 | 16029 |
| 182 and 11 | 2002 |