Least Common Multiple (LCM) of 152 and 195
The least common multiple (LCM) of 152 and 195 is 29640.
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 152 and 195?
First, calculate the GCD of 152 and 195 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 152 ÷ 195 = 0 remainder 152 |
| 2 | 195 ÷ 152 = 1 remainder 43 |
| 3 | 152 ÷ 43 = 3 remainder 23 |
| 4 | 43 ÷ 23 = 1 remainder 20 |
| 5 | 23 ÷ 20 = 1 remainder 3 |
| 6 | 20 ÷ 3 = 6 remainder 2 |
| 7 | 3 ÷ 2 = 1 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 12 and 129 | 516 |
| 200 and 52 | 2600 |
| 103 and 169 | 17407 |
| 159 and 44 | 6996 |
| 76 and 193 | 14668 |