Least Common Multiple (LCM) of 140 and 195
The least common multiple (LCM) of 140 and 195 is 5460.
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 195?
First, calculate the GCD of 140 and 195 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 140 ÷ 195 = 0 remainder 140 |
| 2 | 195 ÷ 140 = 1 remainder 55 |
| 3 | 140 ÷ 55 = 2 remainder 30 |
| 4 | 55 ÷ 30 = 1 remainder 25 |
| 5 | 30 ÷ 25 = 1 remainder 5 |
| 6 | 25 ÷ 5 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 133 and 112 | 2128 |
| 115 and 46 | 230 |
| 98 and 133 | 1862 |
| 104 and 128 | 1664 |
| 159 and 157 | 24963 |