Least Common Multiple (LCM) of 133 and 157
The least common multiple (LCM) of 133 and 157 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 133 and 157?
First, calculate the GCD of 133 and 157 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 133 ÷ 157 = 0 remainder 133 |
| 2 | 157 ÷ 133 = 1 remainder 24 |
| 3 | 133 ÷ 24 = 5 remainder 13 |
| 4 | 24 ÷ 13 = 1 remainder 11 |
| 5 | 13 ÷ 11 = 1 remainder 2 |
| 6 | 11 ÷ 2 = 5 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 115 and 20 | 460 |
| 85 and 56 | 4760 |
| 174 and 200 | 17400 |
| 105 and 161 | 2415 |
| 200 and 174 | 17400 |