Least Common Multiple (LCM) of 157 and 133
The least common multiple (LCM) of 157 and 133 is 20881.
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 157 and 133?
First, calculate the GCD of 157 and 133 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 157 ÷ 133 = 1 remainder 24 |
| 2 | 133 ÷ 24 = 5 remainder 13 |
| 3 | 24 ÷ 13 = 1 remainder 11 |
| 4 | 13 ÷ 11 = 1 remainder 2 |
| 5 | 11 ÷ 2 = 5 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 150 and 65 | 1950 |
| 186 and 58 | 5394 |
| 20 and 105 | 420 |
| 76 and 139 | 10564 |
| 20 and 175 | 700 |