Least Common Multiple (LCM) of 18 and 133
The least common multiple (LCM) of 18 and 133 is 2394.
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 18 and 133?
First, calculate the GCD of 18 and 133 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 18 ÷ 133 = 0 remainder 18 |
| 2 | 133 ÷ 18 = 7 remainder 7 |
| 3 | 18 ÷ 7 = 2 remainder 4 |
| 4 | 7 ÷ 4 = 1 remainder 3 |
| 5 | 4 ÷ 3 = 1 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 133 and 111 | 14763 |
| 36 and 42 | 252 |
| 175 and 32 | 5600 |
| 45 and 169 | 7605 |
| 198 and 128 | 12672 |