Least Common Multiple (LCM) of 199 and 152
The least common multiple (LCM) of 199 and 152 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 199 and 152?
First, calculate the GCD of 199 and 152 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 199 ÷ 152 = 1 remainder 47 |
| 2 | 152 ÷ 47 = 3 remainder 11 |
| 3 | 47 ÷ 11 = 4 remainder 3 |
| 4 | 11 ÷ 3 = 3 remainder 2 |
| 5 | 3 ÷ 2 = 1 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 114 and 132 | 2508 |
| 156 and 77 | 12012 |
| 41 and 80 | 3280 |
| 150 and 196 | 14700 |
| 55 and 70 | 770 |