Least Common Multiple (LCM) of 65 and 136
The least common multiple (LCM) of 65 and 136 is 8840.
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 136?
First, calculate the GCD of 65 and 136 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 65 ÷ 136 = 0 remainder 65 |
| 2 | 136 ÷ 65 = 2 remainder 6 |
| 3 | 65 ÷ 6 = 10 remainder 5 |
| 4 | 6 ÷ 5 = 1 remainder 1 |
| 5 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 129 and 117 | 5031 |
| 41 and 93 | 3813 |
| 68 and 67 | 4556 |
| 112 and 50 | 2800 |
| 64 and 106 | 3392 |