Least Common Multiple (LCM) of 45 and 198
The least common multiple (LCM) of 45 and 198 is 990.
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 45 and 198?
First, calculate the GCD of 45 and 198 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 45 ÷ 198 = 0 remainder 45 |
| 2 | 198 ÷ 45 = 4 remainder 18 |
| 3 | 45 ÷ 18 = 2 remainder 9 |
| 4 | 18 ÷ 9 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 99 and 96 | 3168 |
| 93 and 112 | 10416 |
| 73 and 122 | 8906 |
| 113 and 80 | 9040 |
| 169 and 105 | 17745 |