Least Common Multiple (LCM) of 193 and 140
The least common multiple (LCM) of 193 and 140 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 193 and 140?
First, calculate the GCD of 193 and 140 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 193 ÷ 140 = 1 remainder 53 |
| 2 | 140 ÷ 53 = 2 remainder 34 |
| 3 | 53 ÷ 34 = 1 remainder 19 |
| 4 | 34 ÷ 19 = 1 remainder 15 |
| 5 | 19 ÷ 15 = 1 remainder 4 |
| 6 | 15 ÷ 4 = 3 remainder 3 |
| 7 | 4 ÷ 3 = 1 remainder 1 |
| 8 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 132 and 137 | 18084 |
| 27 and 105 | 945 |
| 98 and 156 | 7644 |
| 119 and 128 | 15232 |
| 131 and 192 | 25152 |