Least Common Multiple (LCM) of 178 and 133
The least common multiple (LCM) of 178 and 133 is 23674.
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 178 and 133?
First, calculate the GCD of 178 and 133 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 178 ÷ 133 = 1 remainder 45 |
| 2 | 133 ÷ 45 = 2 remainder 43 |
| 3 | 45 ÷ 43 = 1 remainder 2 |
| 4 | 43 ÷ 2 = 21 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 47 and 199 | 9353 |
| 181 and 59 | 10679 |
| 77 and 116 | 8932 |
| 138 and 60 | 1380 |
| 15 and 129 | 645 |