Least Common Multiple (LCM) of 154 and 195
The least common multiple (LCM) of 154 and 195 is 30030.
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 154 and 195?
First, calculate the GCD of 154 and 195 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 154 ÷ 195 = 0 remainder 154 |
| 2 | 195 ÷ 154 = 1 remainder 41 |
| 3 | 154 ÷ 41 = 3 remainder 31 |
| 4 | 41 ÷ 31 = 1 remainder 10 |
| 5 | 31 ÷ 10 = 3 remainder 1 |
| 6 | 10 ÷ 1 = 10 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 51 and 151 | 7701 |
| 154 and 91 | 2002 |
| 154 and 189 | 4158 |
| 150 and 106 | 7950 |
| 199 and 83 | 16517 |