Least Common Multiple (LCM) of 195 and 55
The least common multiple (LCM) of 195 and 55 is 2145.
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 195 and 55?
First, calculate the GCD of 195 and 55 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 195 ÷ 55 = 3 remainder 30 |
| 2 | 55 ÷ 30 = 1 remainder 25 |
| 3 | 30 ÷ 25 = 1 remainder 5 |
| 4 | 25 ÷ 5 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 166 and 58 | 4814 |
| 135 and 68 | 9180 |
| 93 and 155 | 465 |
| 112 and 31 | 3472 |
| 54 and 31 | 1674 |