Least Common Multiple (LCM) of 76 and 198
The least common multiple (LCM) of 76 and 198 is 7524.
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 76 and 198?
First, calculate the GCD of 76 and 198 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 76 ÷ 198 = 0 remainder 76 |
| 2 | 198 ÷ 76 = 2 remainder 46 |
| 3 | 76 ÷ 46 = 1 remainder 30 |
| 4 | 46 ÷ 30 = 1 remainder 16 |
| 5 | 30 ÷ 16 = 1 remainder 14 |
| 6 | 16 ÷ 14 = 1 remainder 2 |
| 7 | 14 ÷ 2 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 153 and 150 | 7650 |
| 15 and 172 | 2580 |
| 150 and 16 | 1200 |
| 164 and 189 | 30996 |
| 36 and 116 | 1044 |