Least Common Multiple (LCM) of 133 and 163
The least common multiple (LCM) of 133 and 163 is 21679.
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 163?
First, calculate the GCD of 133 and 163 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 133 ÷ 163 = 0 remainder 133 |
| 2 | 163 ÷ 133 = 1 remainder 30 |
| 3 | 133 ÷ 30 = 4 remainder 13 |
| 4 | 30 ÷ 13 = 2 remainder 4 |
| 5 | 13 ÷ 4 = 3 remainder 1 |
| 6 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 151 and 79 | 11929 |
| 77 and 134 | 10318 |
| 196 and 114 | 11172 |
| 168 and 68 | 2856 |
| 75 and 45 | 225 |