Least Common Multiple (LCM) of 120 and 190
The least common multiple (LCM) of 120 and 190 is 2280.
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 120 and 190?
First, calculate the GCD of 120 and 190 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 120 ÷ 190 = 0 remainder 120 |
| 2 | 190 ÷ 120 = 1 remainder 70 |
| 3 | 120 ÷ 70 = 1 remainder 50 |
| 4 | 70 ÷ 50 = 1 remainder 20 |
| 5 | 50 ÷ 20 = 2 remainder 10 |
| 6 | 20 ÷ 10 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 169 and 147 | 24843 |
| 175 and 118 | 20650 |
| 144 and 168 | 1008 |
| 149 and 199 | 29651 |
| 30 and 159 | 1590 |