Least Common Multiple (LCM) of 197 and 142
The least common multiple (LCM) of 197 and 142 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 197 and 142?
First, calculate the GCD of 197 and 142 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 197 ÷ 142 = 1 remainder 55 |
| 2 | 142 ÷ 55 = 2 remainder 32 |
| 3 | 55 ÷ 32 = 1 remainder 23 |
| 4 | 32 ÷ 23 = 1 remainder 9 |
| 5 | 23 ÷ 9 = 2 remainder 5 |
| 6 | 9 ÷ 5 = 1 remainder 4 |
| 7 | 5 ÷ 4 = 1 remainder 1 |
| 8 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 169 and 148 | 25012 |
| 172 and 42 | 3612 |
| 139 and 12 | 1668 |
| 120 and 66 | 1320 |
| 18 and 101 | 1818 |