Least Common Multiple (LCM) of 88 and 199
The least common multiple (LCM) of 88 and 199 is 17512.
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 88 and 199?
First, calculate the GCD of 88 and 199 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 88 ÷ 199 = 0 remainder 88 |
| 2 | 199 ÷ 88 = 2 remainder 23 |
| 3 | 88 ÷ 23 = 3 remainder 19 |
| 4 | 23 ÷ 19 = 1 remainder 4 |
| 5 | 19 ÷ 4 = 4 remainder 3 |
| 6 | 4 ÷ 3 = 1 remainder 1 |
| 7 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 30 and 144 | 720 |
| 139 and 89 | 12371 |
| 81 and 64 | 5184 |
| 129 and 197 | 25413 |
| 65 and 181 | 11765 |