Least Common Multiple (LCM) of 171 and 132
The least common multiple (LCM) of 171 and 132 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 171 and 132?
First, calculate the GCD of 171 and 132 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 171 ÷ 132 = 1 remainder 39 |
| 2 | 132 ÷ 39 = 3 remainder 15 |
| 3 | 39 ÷ 15 = 2 remainder 9 |
| 4 | 15 ÷ 9 = 1 remainder 6 |
| 5 | 9 ÷ 6 = 1 remainder 3 |
| 6 | 6 ÷ 3 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 49 and 169 | 8281 |
| 133 and 183 | 24339 |
| 186 and 135 | 8370 |
| 105 and 143 | 15015 |
| 66 and 39 | 858 |