Least Common Multiple (LCM) of 119 and 133
The least common multiple (LCM) of 119 and 133 is 2261.
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 119 and 133?
First, calculate the GCD of 119 and 133 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 119 ÷ 133 = 0 remainder 119 |
| 2 | 133 ÷ 119 = 1 remainder 14 |
| 3 | 119 ÷ 14 = 8 remainder 7 |
| 4 | 14 ÷ 7 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 21 and 14 | 42 |
| 154 and 103 | 15862 |
| 183 and 72 | 4392 |
| 67 and 175 | 11725 |
| 61 and 105 | 6405 |