Least Common Multiple (LCM) of 85 and 106
The least common multiple (LCM) of 85 and 106 is 9010.
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 106?
First, calculate the GCD of 85 and 106 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 85 ÷ 106 = 0 remainder 85 |
| 2 | 106 ÷ 85 = 1 remainder 21 |
| 3 | 85 ÷ 21 = 4 remainder 1 |
| 4 | 21 ÷ 1 = 21 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 83 and 89 | 7387 |
| 45 and 120 | 360 |
| 186 and 75 | 4650 |
| 34 and 87 | 2958 |
| 132 and 106 | 6996 |