Least Common Multiple (LCM) of 65 and 188
The least common multiple (LCM) of 65 and 188 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 65 and 188?
First, calculate the GCD of 65 and 188 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 65 ÷ 188 = 0 remainder 65 |
| 2 | 188 ÷ 65 = 2 remainder 58 |
| 3 | 65 ÷ 58 = 1 remainder 7 |
| 4 | 58 ÷ 7 = 8 remainder 2 |
| 5 | 7 ÷ 2 = 3 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 66 and 86 | 2838 |
| 102 and 133 | 13566 |
| 36 and 136 | 1224 |
| 182 and 58 | 5278 |
| 98 and 38 | 1862 |