Least Common Multiple (LCM) of 101 and 188
The least common multiple (LCM) of 101 and 188 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 101 and 188?
First, calculate the GCD of 101 and 188 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 101 ÷ 188 = 0 remainder 101 |
| 2 | 188 ÷ 101 = 1 remainder 87 |
| 3 | 101 ÷ 87 = 1 remainder 14 |
| 4 | 87 ÷ 14 = 6 remainder 3 |
| 5 | 14 ÷ 3 = 4 remainder 2 |
| 6 | 3 ÷ 2 = 1 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 120 and 79 | 9480 |
| 151 and 151 | 151 |
| 83 and 57 | 4731 |
| 99 and 120 | 3960 |
| 105 and 87 | 3045 |