Least Common Multiple (LCM) of 65 and 137
The least common multiple (LCM) of 65 and 137 is 8905.
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 137?
First, calculate the GCD of 65 and 137 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 65 ÷ 137 = 0 remainder 65 |
| 2 | 137 ÷ 65 = 2 remainder 7 |
| 3 | 65 ÷ 7 = 9 remainder 2 |
| 4 | 7 ÷ 2 = 3 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 67 and 127 | 8509 |
| 80 and 132 | 2640 |
| 112 and 35 | 560 |
| 187 and 51 | 561 |
| 97 and 72 | 6984 |