Least Common Multiple (LCM) of 146 and 199
The least common multiple (LCM) of 146 and 199 is 29054.
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 146 and 199?
First, calculate the GCD of 146 and 199 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 146 ÷ 199 = 0 remainder 146 |
| 2 | 199 ÷ 146 = 1 remainder 53 |
| 3 | 146 ÷ 53 = 2 remainder 40 |
| 4 | 53 ÷ 40 = 1 remainder 13 |
| 5 | 40 ÷ 13 = 3 remainder 1 |
| 6 | 13 ÷ 1 = 13 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 195 and 112 | 21840 |
| 167 and 143 | 23881 |
| 172 and 115 | 19780 |
| 72 and 133 | 9576 |
| 140 and 23 | 3220 |