Least Common Multiple (LCM) of 133 and 149
The least common multiple (LCM) of 133 and 149 is 19817.
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 149?
First, calculate the GCD of 133 and 149 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 133 ÷ 149 = 0 remainder 133 |
| 2 | 149 ÷ 133 = 1 remainder 16 |
| 3 | 133 ÷ 16 = 8 remainder 5 |
| 4 | 16 ÷ 5 = 3 remainder 1 |
| 5 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 144 and 102 | 2448 |
| 107 and 83 | 8881 |
| 96 and 67 | 6432 |
| 172 and 199 | 34228 |
| 114 and 193 | 22002 |