Least Common Multiple (LCM) of 85 and 116
The least common multiple (LCM) of 85 and 116 is 9860.
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 116?
First, calculate the GCD of 85 and 116 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 85 ÷ 116 = 0 remainder 85 |
| 2 | 116 ÷ 85 = 1 remainder 31 |
| 3 | 85 ÷ 31 = 2 remainder 23 |
| 4 | 31 ÷ 23 = 1 remainder 8 |
| 5 | 23 ÷ 8 = 2 remainder 7 |
| 6 | 8 ÷ 7 = 1 remainder 1 |
| 7 | 7 ÷ 1 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 13 and 117 | 117 |
| 87 and 45 | 1305 |
| 108 and 37 | 3996 |
| 45 and 138 | 2070 |
| 161 and 34 | 5474 |