Least Common Multiple (LCM) of 199 and 147
The least common multiple (LCM) of 199 and 147 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 199 and 147?
First, calculate the GCD of 199 and 147 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 199 ÷ 147 = 1 remainder 52 |
| 2 | 147 ÷ 52 = 2 remainder 43 |
| 3 | 52 ÷ 43 = 1 remainder 9 |
| 4 | 43 ÷ 9 = 4 remainder 7 |
| 5 | 9 ÷ 7 = 1 remainder 2 |
| 6 | 7 ÷ 2 = 3 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 147 and 75 | 3675 |
| 112 and 71 | 7952 |
| 176 and 196 | 8624 |
| 109 and 120 | 13080 |
| 106 and 35 | 3710 |