Least Common Multiple (LCM) of 168 and 195
The least common multiple (LCM) of 168 and 195 is 10920.
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 168 and 195?
First, calculate the GCD of 168 and 195 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 168 ÷ 195 = 0 remainder 168 |
| 2 | 195 ÷ 168 = 1 remainder 27 |
| 3 | 168 ÷ 27 = 6 remainder 6 |
| 4 | 27 ÷ 6 = 4 remainder 3 |
| 5 | 6 ÷ 3 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 57 and 165 | 3135 |
| 68 and 153 | 612 |
| 126 and 96 | 2016 |
| 196 and 19 | 3724 |
| 126 and 49 | 882 |