Least Common Multiple (LCM) of 142 and 193
The least common multiple (LCM) of 142 and 193 is 27406.
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 142 and 193?
First, calculate the GCD of 142 and 193 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 142 ÷ 193 = 0 remainder 142 |
| 2 | 193 ÷ 142 = 1 remainder 51 |
| 3 | 142 ÷ 51 = 2 remainder 40 |
| 4 | 51 ÷ 40 = 1 remainder 11 |
| 5 | 40 ÷ 11 = 3 remainder 7 |
| 6 | 11 ÷ 7 = 1 remainder 4 |
| 7 | 7 ÷ 4 = 1 remainder 3 |
| 8 | 4 ÷ 3 = 1 remainder 1 |
| 9 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 39 and 69 | 897 |
| 82 and 173 | 14186 |
| 32 and 82 | 1312 |
| 19 and 109 | 2071 |
| 144 and 195 | 9360 |