Least Common Multiple (LCM) of 147 and 199
The least common multiple (LCM) of 147 and 199 is 29253.
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 147 and 199?
First, calculate the GCD of 147 and 199 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 147 ÷ 199 = 0 remainder 147 |
| 2 | 199 ÷ 147 = 1 remainder 52 |
| 3 | 147 ÷ 52 = 2 remainder 43 |
| 4 | 52 ÷ 43 = 1 remainder 9 |
| 5 | 43 ÷ 9 = 4 remainder 7 |
| 6 | 9 ÷ 7 = 1 remainder 2 |
| 7 | 7 ÷ 2 = 3 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 32 and 200 | 800 |
| 187 and 92 | 17204 |
| 84 and 88 | 1848 |
| 108 and 199 | 21492 |
| 126 and 192 | 4032 |