Least Common Multiple (LCM) of 65 and 187
The least common multiple (LCM) of 65 and 187 is 12155.
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 187?
First, calculate the GCD of 65 and 187 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 65 ÷ 187 = 0 remainder 65 |
| 2 | 187 ÷ 65 = 2 remainder 57 |
| 3 | 65 ÷ 57 = 1 remainder 8 |
| 4 | 57 ÷ 8 = 7 remainder 1 |
| 5 | 8 ÷ 1 = 8 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 89 and 69 | 6141 |
| 105 and 90 | 630 |
| 159 and 22 | 3498 |
| 48 and 63 | 1008 |
| 47 and 32 | 1504 |