Least Common Multiple (LCM) of 65 and 121
The least common multiple (LCM) of 65 and 121 is 7865.
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 121?
First, calculate the GCD of 65 and 121 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 65 ÷ 121 = 0 remainder 65 |
| 2 | 121 ÷ 65 = 1 remainder 56 |
| 3 | 65 ÷ 56 = 1 remainder 9 |
| 4 | 56 ÷ 9 = 6 remainder 2 |
| 5 | 9 ÷ 2 = 4 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 69 and 194 | 13386 |
| 177 and 119 | 21063 |
| 193 and 79 | 15247 |
| 75 and 120 | 600 |
| 105 and 109 | 11445 |