Least Common Multiple (LCM) of 20 and 119
The least common multiple (LCM) of 20 and 119 is 2380.
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 20 and 119?
First, calculate the GCD of 20 and 119 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 20 ÷ 119 = 0 remainder 20 |
| 2 | 119 ÷ 20 = 5 remainder 19 |
| 3 | 20 ÷ 19 = 1 remainder 1 |
| 4 | 19 ÷ 1 = 19 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 110 and 140 | 1540 |
| 161 and 99 | 15939 |
| 34 and 110 | 1870 |
| 159 and 22 | 3498 |
| 112 and 180 | 5040 |