Least Common Multiple (LCM) of 65 and 124
The least common multiple (LCM) of 65 and 124 is 8060.
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 124?
First, calculate the GCD of 65 and 124 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 65 ÷ 124 = 0 remainder 65 |
| 2 | 124 ÷ 65 = 1 remainder 59 |
| 3 | 65 ÷ 59 = 1 remainder 6 |
| 4 | 59 ÷ 6 = 9 remainder 5 |
| 5 | 6 ÷ 5 = 1 remainder 1 |
| 6 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 45 and 81 | 405 |
| 115 and 45 | 1035 |
| 184 and 56 | 1288 |
| 107 and 56 | 5992 |
| 175 and 66 | 11550 |