Least Common Multiple (LCM) of 188 and 101
The least common multiple (LCM) of 188 and 101 is 18988.
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 188 and 101?
First, calculate the GCD of 188 and 101 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 188 ÷ 101 = 1 remainder 87 |
| 2 | 101 ÷ 87 = 1 remainder 14 |
| 3 | 87 ÷ 14 = 6 remainder 3 |
| 4 | 14 ÷ 3 = 4 remainder 2 |
| 5 | 3 ÷ 2 = 1 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 89 and 189 | 16821 |
| 30 and 61 | 1830 |
| 110 and 85 | 1870 |
| 125 and 124 | 15500 |
| 42 and 61 | 2562 |