Least Common Multiple (LCM) of 156 and 198
The least common multiple (LCM) of 156 and 198 is 5148.
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 156 and 198?
First, calculate the GCD of 156 and 198 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 156 ÷ 198 = 0 remainder 156 |
| 2 | 198 ÷ 156 = 1 remainder 42 |
| 3 | 156 ÷ 42 = 3 remainder 30 |
| 4 | 42 ÷ 30 = 1 remainder 12 |
| 5 | 30 ÷ 12 = 2 remainder 6 |
| 6 | 12 ÷ 6 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 21 and 21 | 21 |
| 12 and 21 | 84 |
| 49 and 35 | 245 |
| 72 and 71 | 5112 |
| 198 and 101 | 19998 |