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 |
|---|---|
| 89 and 172 | 15308 |
| 154 and 78 | 6006 |
| 145 and 174 | 870 |
| 16 and 137 | 2192 |
| 120 and 94 | 5640 |