Least Common Multiple (LCM) of 69 and 195
The least common multiple (LCM) of 69 and 195 is 4485.
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 69 and 195?
First, calculate the GCD of 69 and 195 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 69 ÷ 195 = 0 remainder 69 |
| 2 | 195 ÷ 69 = 2 remainder 57 |
| 3 | 69 ÷ 57 = 1 remainder 12 |
| 4 | 57 ÷ 12 = 4 remainder 9 |
| 5 | 12 ÷ 9 = 1 remainder 3 |
| 6 | 9 ÷ 3 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 102 and 75 | 2550 |
| 106 and 194 | 10282 |
| 165 and 144 | 7920 |
| 121 and 186 | 22506 |
| 170 and 150 | 2550 |