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 |
|---|---|
| 195 and 51 | 3315 |
| 195 and 104 | 1560 |
| 35 and 24 | 840 |
| 149 and 101 | 15049 |
| 65 and 106 | 6890 |