Least Common Multiple (LCM) of 195 and 153
The least common multiple (LCM) of 195 and 153 is 9945.
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 153?
First, calculate the GCD of 195 and 153 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 195 ÷ 153 = 1 remainder 42 |
| 2 | 153 ÷ 42 = 3 remainder 27 |
| 3 | 42 ÷ 27 = 1 remainder 15 |
| 4 | 27 ÷ 15 = 1 remainder 12 |
| 5 | 15 ÷ 12 = 1 remainder 3 |
| 6 | 12 ÷ 3 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 42 and 148 | 3108 |
| 134 and 96 | 6432 |
| 72 and 60 | 360 |
| 195 and 128 | 24960 |
| 176 and 172 | 7568 |