Least Common Multiple (LCM) of 142 and 197
The least common multiple (LCM) of 142 and 197 is 27974.
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 197?
First, calculate the GCD of 142 and 197 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 142 ÷ 197 = 0 remainder 142 |
| 2 | 197 ÷ 142 = 1 remainder 55 |
| 3 | 142 ÷ 55 = 2 remainder 32 |
| 4 | 55 ÷ 32 = 1 remainder 23 |
| 5 | 32 ÷ 23 = 1 remainder 9 |
| 6 | 23 ÷ 9 = 2 remainder 5 |
| 7 | 9 ÷ 5 = 1 remainder 4 |
| 8 | 5 ÷ 4 = 1 remainder 1 |
| 9 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 100 and 86 | 4300 |
| 195 and 162 | 10530 |
| 174 and 86 | 7482 |
| 19 and 173 | 3287 |
| 137 and 172 | 23564 |