Least Common Multiple (LCM) of 120 and 195
The least common multiple (LCM) of 120 and 195 is 1560.
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 195?
First, calculate the GCD of 120 and 195 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 120 ÷ 195 = 0 remainder 120 |
| 2 | 195 ÷ 120 = 1 remainder 75 |
| 3 | 120 ÷ 75 = 1 remainder 45 |
| 4 | 75 ÷ 45 = 1 remainder 30 |
| 5 | 45 ÷ 30 = 1 remainder 15 |
| 6 | 30 ÷ 15 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 163 and 180 | 29340 |
| 142 and 128 | 9088 |
| 15 and 64 | 960 |
| 33 and 56 | 1848 |
| 25 and 67 | 1675 |