Least Common Multiple (LCM) of 169 and 133
The least common multiple (LCM) of 169 and 133 is 22477.
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 169 and 133?
First, calculate the GCD of 169 and 133 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 169 ÷ 133 = 1 remainder 36 |
| 2 | 133 ÷ 36 = 3 remainder 25 |
| 3 | 36 ÷ 25 = 1 remainder 11 |
| 4 | 25 ÷ 11 = 2 remainder 3 |
| 5 | 11 ÷ 3 = 3 remainder 2 |
| 6 | 3 ÷ 2 = 1 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 131 and 128 | 16768 |
| 174 and 139 | 24186 |
| 105 and 177 | 6195 |
| 171 and 83 | 14193 |
| 171 and 82 | 14022 |