Least Common Multiple (LCM) of 85 and 124
The least common multiple (LCM) of 85 and 124 is 10540.
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 85 and 124?
First, calculate the GCD of 85 and 124 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 85 ÷ 124 = 0 remainder 85 |
| 2 | 124 ÷ 85 = 1 remainder 39 |
| 3 | 85 ÷ 39 = 2 remainder 7 |
| 4 | 39 ÷ 7 = 5 remainder 4 |
| 5 | 7 ÷ 4 = 1 remainder 3 |
| 6 | 4 ÷ 3 = 1 remainder 1 |
| 7 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 177 and 54 | 3186 |
| 200 and 87 | 17400 |
| 161 and 66 | 10626 |
| 100 and 123 | 12300 |
| 113 and 176 | 19888 |