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 |
|---|---|
| 17 and 32 | 544 |
| 171 and 10 | 1710 |
| 196 and 195 | 38220 |
| 21 and 112 | 336 |
| 105 and 121 | 12705 |