Least Common Multiple (LCM) of 152 and 199
The least common multiple (LCM) of 152 and 199 is 30248.
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 152 and 199?
First, calculate the GCD of 152 and 199 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 152 ÷ 199 = 0 remainder 152 |
| 2 | 199 ÷ 152 = 1 remainder 47 |
| 3 | 152 ÷ 47 = 3 remainder 11 |
| 4 | 47 ÷ 11 = 4 remainder 3 |
| 5 | 11 ÷ 3 = 3 remainder 2 |
| 6 | 3 ÷ 2 = 1 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 196 and 162 | 15876 |
| 133 and 130 | 17290 |
| 58 and 21 | 1218 |
| 106 and 65 | 6890 |
| 36 and 152 | 1368 |