Least Common Multiple (LCM) of 112 and 133
The least common multiple (LCM) of 112 and 133 is 2128.
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 112 and 133?
First, calculate the GCD of 112 and 133 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 112 ÷ 133 = 0 remainder 112 |
| 2 | 133 ÷ 112 = 1 remainder 21 |
| 3 | 112 ÷ 21 = 5 remainder 7 |
| 4 | 21 ÷ 7 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 17 and 20 | 340 |
| 54 and 186 | 1674 |
| 185 and 181 | 33485 |
| 53 and 82 | 4346 |
| 33 and 67 | 2211 |