Least Common Multiple (LCM) of 140 and 193
The least common multiple (LCM) of 140 and 193 is 27020.
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 193?
First, calculate the GCD of 140 and 193 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 140 ÷ 193 = 0 remainder 140 |
| 2 | 193 ÷ 140 = 1 remainder 53 |
| 3 | 140 ÷ 53 = 2 remainder 34 |
| 4 | 53 ÷ 34 = 1 remainder 19 |
| 5 | 34 ÷ 19 = 1 remainder 15 |
| 6 | 19 ÷ 15 = 1 remainder 4 |
| 7 | 15 ÷ 4 = 3 remainder 3 |
| 8 | 4 ÷ 3 = 1 remainder 1 |
| 9 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 24 and 85 | 2040 |
| 27 and 119 | 3213 |
| 79 and 80 | 6320 |
| 118 and 36 | 2124 |
| 114 and 119 | 13566 |