Least Common Multiple (LCM) of 85 and 117
The least common multiple (LCM) of 85 and 117 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 85 and 117?
First, calculate the GCD of 85 and 117 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 85 ÷ 117 = 0 remainder 85 |
| 2 | 117 ÷ 85 = 1 remainder 32 |
| 3 | 85 ÷ 32 = 2 remainder 21 |
| 4 | 32 ÷ 21 = 1 remainder 11 |
| 5 | 21 ÷ 11 = 1 remainder 10 |
| 6 | 11 ÷ 10 = 1 remainder 1 |
| 7 | 10 ÷ 1 = 10 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 147 and 25 | 3675 |
| 78 and 116 | 4524 |
| 126 and 55 | 6930 |
| 87 and 77 | 6699 |
| 79 and 109 | 8611 |