Least Common Multiple (LCM) of 72 and 195
The least common multiple (LCM) of 72 and 195 is 4680.
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 72 and 195?
First, calculate the GCD of 72 and 195 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 72 ÷ 195 = 0 remainder 72 |
| 2 | 195 ÷ 72 = 2 remainder 51 |
| 3 | 72 ÷ 51 = 1 remainder 21 |
| 4 | 51 ÷ 21 = 2 remainder 9 |
| 5 | 21 ÷ 9 = 2 remainder 3 |
| 6 | 9 ÷ 3 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 155 and 110 | 3410 |
| 189 and 104 | 19656 |
| 65 and 194 | 12610 |
| 40 and 185 | 1480 |
| 186 and 140 | 13020 |