Least Common Multiple (LCM) of 198 and 76
The least common multiple (LCM) of 198 and 76 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 198 and 76?
First, calculate the GCD of 198 and 76 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 198 ÷ 76 = 2 remainder 46 |
| 2 | 76 ÷ 46 = 1 remainder 30 |
| 3 | 46 ÷ 30 = 1 remainder 16 |
| 4 | 30 ÷ 16 = 1 remainder 14 |
| 5 | 16 ÷ 14 = 1 remainder 2 |
| 6 | 14 ÷ 2 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 172 and 31 | 5332 |
| 182 and 115 | 20930 |
| 82 and 66 | 2706 |
| 50 and 148 | 3700 |
| 152 and 62 | 4712 |