Least Common Multiple (LCM) of 11 and 65
The least common multiple (LCM) of 11 and 65 is 715.
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 11 and 65?
First, calculate the GCD of 11 and 65 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 11 ÷ 65 = 0 remainder 11 |
| 2 | 65 ÷ 11 = 5 remainder 10 |
| 3 | 11 ÷ 10 = 1 remainder 1 |
| 4 | 10 ÷ 1 = 10 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 122 and 63 | 7686 |
| 119 and 198 | 23562 |
| 55 and 150 | 1650 |
| 43 and 27 | 1161 |
| 118 and 38 | 2242 |