Least Common Multiple (LCM) of 117 and 85
The least common multiple (LCM) of 117 and 85 is 9945.
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 117 and 85?
First, calculate the GCD of 117 and 85 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 117 ÷ 85 = 1 remainder 32 |
| 2 | 85 ÷ 32 = 2 remainder 21 |
| 3 | 32 ÷ 21 = 1 remainder 11 |
| 4 | 21 ÷ 11 = 1 remainder 10 |
| 5 | 11 ÷ 10 = 1 remainder 1 |
| 6 | 10 ÷ 1 = 10 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 35 and 175 | 175 |
| 134 and 122 | 8174 |
| 12 and 96 | 96 |
| 107 and 189 | 20223 |
| 102 and 30 | 510 |