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 |
|---|---|
| 110 and 136 | 7480 |
| 129 and 108 | 4644 |
| 45 and 191 | 8595 |
| 167 and 116 | 19372 |
| 61 and 79 | 4819 |