Least Common Multiple (LCM) of 119 and 19
The least common multiple (LCM) of 119 and 19 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 19?
First, calculate the GCD of 119 and 19 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 119 ÷ 19 = 6 remainder 5 |
| 2 | 19 ÷ 5 = 3 remainder 4 |
| 3 | 5 ÷ 4 = 1 remainder 1 |
| 4 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 57 and 192 | 3648 |
| 20 and 56 | 280 |
| 112 and 40 | 560 |
| 121 and 41 | 4961 |
| 169 and 182 | 2366 |