Least Common Multiple (LCM) of 99 and 85
The least common multiple (LCM) of 99 and 85 is 8415.
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 99 and 85?
First, calculate the GCD of 99 and 85 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 99 ÷ 85 = 1 remainder 14 |
| 2 | 85 ÷ 14 = 6 remainder 1 |
| 3 | 14 ÷ 1 = 14 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 58 and 121 | 7018 |
| 77 and 23 | 1771 |
| 35 and 96 | 3360 |
| 36 and 82 | 1476 |
| 132 and 132 | 132 |