Least Common Multiple (LCM) of 145 and 198
The least common multiple (LCM) of 145 and 198 is 28710.
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 145 and 198?
First, calculate the GCD of 145 and 198 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 145 ÷ 198 = 0 remainder 145 |
| 2 | 198 ÷ 145 = 1 remainder 53 |
| 3 | 145 ÷ 53 = 2 remainder 39 |
| 4 | 53 ÷ 39 = 1 remainder 14 |
| 5 | 39 ÷ 14 = 2 remainder 11 |
| 6 | 14 ÷ 11 = 1 remainder 3 |
| 7 | 11 ÷ 3 = 3 remainder 2 |
| 8 | 3 ÷ 2 = 1 remainder 1 |
| 9 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 108 and 195 | 7020 |
| 161 and 134 | 21574 |
| 191 and 172 | 32852 |
| 26 and 45 | 1170 |
| 170 and 40 | 680 |