Least Common Multiple (LCM) of 133 and 197
The least common multiple (LCM) of 133 and 197 is 26201.
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 133 and 197?
First, calculate the GCD of 133 and 197 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 133 ÷ 197 = 0 remainder 133 |
| 2 | 197 ÷ 133 = 1 remainder 64 |
| 3 | 133 ÷ 64 = 2 remainder 5 |
| 4 | 64 ÷ 5 = 12 remainder 4 |
| 5 | 5 ÷ 4 = 1 remainder 1 |
| 6 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 102 and 153 | 306 |
| 109 and 156 | 17004 |
| 72 and 18 | 72 |
| 142 and 167 | 23714 |
| 29 and 80 | 2320 |