Least Common Multiple (LCM) of 140 and 171
The least common multiple (LCM) of 140 and 171 is 23940.
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 140 and 171?
First, calculate the GCD of 140 and 171 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 140 ÷ 171 = 0 remainder 140 |
| 2 | 171 ÷ 140 = 1 remainder 31 |
| 3 | 140 ÷ 31 = 4 remainder 16 |
| 4 | 31 ÷ 16 = 1 remainder 15 |
| 5 | 16 ÷ 15 = 1 remainder 1 |
| 6 | 15 ÷ 1 = 15 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 146 and 81 | 11826 |
| 110 and 149 | 16390 |
| 57 and 29 | 1653 |
| 189 and 49 | 1323 |
| 41 and 138 | 5658 |