Least Common Multiple (LCM) of 81 and 140
The least common multiple (LCM) of 81 and 140 is 11340.
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 81 and 140?
First, calculate the GCD of 81 and 140 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 81 ÷ 140 = 0 remainder 81 |
| 2 | 140 ÷ 81 = 1 remainder 59 |
| 3 | 81 ÷ 59 = 1 remainder 22 |
| 4 | 59 ÷ 22 = 2 remainder 15 |
| 5 | 22 ÷ 15 = 1 remainder 7 |
| 6 | 15 ÷ 7 = 2 remainder 1 |
| 7 | 7 ÷ 1 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 125 and 70 | 1750 |
| 188 and 90 | 8460 |
| 162 and 167 | 27054 |
| 128 and 113 | 14464 |
| 136 and 78 | 5304 |