Least Common Multiple (LCM) of 101 and 199
The least common multiple (LCM) of 101 and 199 is 20099.
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 101 and 199?
First, calculate the GCD of 101 and 199 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 101 ÷ 199 = 0 remainder 101 |
| 2 | 199 ÷ 101 = 1 remainder 98 |
| 3 | 101 ÷ 98 = 1 remainder 3 |
| 4 | 98 ÷ 3 = 32 remainder 2 |
| 5 | 3 ÷ 2 = 1 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 54 and 113 | 6102 |
| 37 and 95 | 3515 |
| 87 and 23 | 2001 |
| 89 and 175 | 15575 |
| 12 and 31 | 372 |