Least Common Multiple (LCM) of 150 and 195
The least common multiple (LCM) of 150 and 195 is 1950.
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 150 and 195?
First, calculate the GCD of 150 and 195 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 150 ÷ 195 = 0 remainder 150 |
| 2 | 195 ÷ 150 = 1 remainder 45 |
| 3 | 150 ÷ 45 = 3 remainder 15 |
| 4 | 45 ÷ 15 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 32 and 82 | 1312 |
| 154 and 45 | 6930 |
| 169 and 164 | 27716 |
| 122 and 36 | 2196 |
| 127 and 23 | 2921 |