Least Common Multiple (LCM) of 65 and 123
The least common multiple (LCM) of 65 and 123 is 7995.
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 123?
First, calculate the GCD of 65 and 123 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 65 ÷ 123 = 0 remainder 65 |
| 2 | 123 ÷ 65 = 1 remainder 58 |
| 3 | 65 ÷ 58 = 1 remainder 7 |
| 4 | 58 ÷ 7 = 8 remainder 2 |
| 5 | 7 ÷ 2 = 3 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 32 and 123 | 3936 |
| 49 and 123 | 6027 |
| 116 and 36 | 1044 |
| 82 and 143 | 11726 |
| 27 and 185 | 4995 |