Least Common Multiple (LCM) of 85 and 114
The least common multiple (LCM) of 85 and 114 is 9690.
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 114?
First, calculate the GCD of 85 and 114 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 85 ÷ 114 = 0 remainder 85 |
| 2 | 114 ÷ 85 = 1 remainder 29 |
| 3 | 85 ÷ 29 = 2 remainder 27 |
| 4 | 29 ÷ 27 = 1 remainder 2 |
| 5 | 27 ÷ 2 = 13 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 112 and 60 | 1680 |
| 104 and 181 | 18824 |
| 24 and 53 | 1272 |
| 117 and 32 | 3744 |
| 121 and 59 | 7139 |