Least Common Multiple (LCM) of 188 and 65
The least common multiple (LCM) of 188 and 65 is 12220.
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 65?
First, calculate the GCD of 188 and 65 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 188 ÷ 65 = 2 remainder 58 |
| 2 | 65 ÷ 58 = 1 remainder 7 |
| 3 | 58 ÷ 7 = 8 remainder 2 |
| 4 | 7 ÷ 2 = 3 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 182 and 45 | 8190 |
| 132 and 133 | 17556 |
| 111 and 18 | 666 |
| 139 and 193 | 26827 |
| 78 and 11 | 858 |