Least Common Multiple (LCM) of 85 and 113
The least common multiple (LCM) of 85 and 113 is 9605.
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 113?
First, calculate the GCD of 85 and 113 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 85 ÷ 113 = 0 remainder 85 |
| 2 | 113 ÷ 85 = 1 remainder 28 |
| 3 | 85 ÷ 28 = 3 remainder 1 |
| 4 | 28 ÷ 1 = 28 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 134 and 147 | 19698 |
| 166 and 170 | 14110 |
| 55 and 81 | 4455 |
| 155 and 179 | 27745 |
| 152 and 133 | 1064 |