Least Common Multiple (LCM) of 65 and 92
The least common multiple (LCM) of 65 and 92 is 5980.
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 92?
First, calculate the GCD of 65 and 92 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 65 ÷ 92 = 0 remainder 65 |
| 2 | 92 ÷ 65 = 1 remainder 27 |
| 3 | 65 ÷ 27 = 2 remainder 11 |
| 4 | 27 ÷ 11 = 2 remainder 5 |
| 5 | 11 ÷ 5 = 2 remainder 1 |
| 6 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 100 and 117 | 11700 |
| 50 and 164 | 4100 |
| 20 and 74 | 740 |
| 68 and 190 | 6460 |
| 166 and 184 | 15272 |