Least Common Multiple (LCM) of 85 and 101
The least common multiple (LCM) of 85 and 101 is 8585.
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 101?
First, calculate the GCD of 85 and 101 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 85 ÷ 101 = 0 remainder 85 |
| 2 | 101 ÷ 85 = 1 remainder 16 |
| 3 | 85 ÷ 16 = 5 remainder 5 |
| 4 | 16 ÷ 5 = 3 remainder 1 |
| 5 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 93 and 75 | 2325 |
| 73 and 122 | 8906 |
| 19 and 63 | 1197 |
| 62 and 72 | 2232 |
| 161 and 129 | 20769 |