Least Common Multiple (LCM) of 133 and 23
The least common multiple (LCM) of 133 and 23 is 3059.
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 23?
First, calculate the GCD of 133 and 23 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 133 ÷ 23 = 5 remainder 18 |
| 2 | 23 ÷ 18 = 1 remainder 5 |
| 3 | 18 ÷ 5 = 3 remainder 3 |
| 4 | 5 ÷ 3 = 1 remainder 2 |
| 5 | 3 ÷ 2 = 1 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 60 and 82 | 2460 |
| 164 and 113 | 18532 |
| 199 and 184 | 36616 |
| 85 and 26 | 2210 |
| 24 and 54 | 216 |