Least Common Multiple (LCM) of 152 and 198
The least common multiple (LCM) of 152 and 198 is 15048.
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 198?
First, calculate the GCD of 152 and 198 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 152 ÷ 198 = 0 remainder 152 |
| 2 | 198 ÷ 152 = 1 remainder 46 |
| 3 | 152 ÷ 46 = 3 remainder 14 |
| 4 | 46 ÷ 14 = 3 remainder 4 |
| 5 | 14 ÷ 4 = 3 remainder 2 |
| 6 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 43 and 196 | 8428 |
| 15 and 100 | 300 |
| 10 and 15 | 30 |
| 135 and 85 | 2295 |
| 70 and 135 | 1890 |