Least Common Multiple (LCM) of 102 and 65
The least common multiple (LCM) of 102 and 65 is 6630.
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 102 and 65?
First, calculate the GCD of 102 and 65 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 102 ÷ 65 = 1 remainder 37 |
| 2 | 65 ÷ 37 = 1 remainder 28 |
| 3 | 37 ÷ 28 = 1 remainder 9 |
| 4 | 28 ÷ 9 = 3 remainder 1 |
| 5 | 9 ÷ 1 = 9 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 15 and 180 | 180 |
| 129 and 116 | 14964 |
| 10 and 28 | 140 |
| 198 and 140 | 13860 |
| 145 and 53 | 7685 |