Least Common Multiple (LCM) of 108 and 171
The least common multiple (LCM) of 108 and 171 is 2052.
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 108 and 171?
First, calculate the GCD of 108 and 171 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 108 ÷ 171 = 0 remainder 108 |
| 2 | 171 ÷ 108 = 1 remainder 63 |
| 3 | 108 ÷ 63 = 1 remainder 45 |
| 4 | 63 ÷ 45 = 1 remainder 18 |
| 5 | 45 ÷ 18 = 2 remainder 9 |
| 6 | 18 ÷ 9 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 35 and 100 | 700 |
| 132 and 147 | 6468 |
| 112 and 167 | 18704 |
| 53 and 157 | 8321 |
| 127 and 115 | 14605 |