Least Common Multiple (LCM) of 133 and 138
The least common multiple (LCM) of 133 and 138 is 18354.
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 138?
First, calculate the GCD of 133 and 138 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 133 ÷ 138 = 0 remainder 133 |
| 2 | 138 ÷ 133 = 1 remainder 5 |
| 3 | 133 ÷ 5 = 26 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 |
|---|---|
| 120 and 186 | 3720 |
| 187 and 100 | 18700 |
| 25 and 153 | 3825 |
| 19 and 116 | 2204 |
| 192 and 51 | 3264 |