Least Common Multiple (LCM) of 85 and 137
The least common multiple (LCM) of 85 and 137 is 11645.
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 137?
First, calculate the GCD of 85 and 137 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 85 ÷ 137 = 0 remainder 85 |
| 2 | 137 ÷ 85 = 1 remainder 52 |
| 3 | 85 ÷ 52 = 1 remainder 33 |
| 4 | 52 ÷ 33 = 1 remainder 19 |
| 5 | 33 ÷ 19 = 1 remainder 14 |
| 6 | 19 ÷ 14 = 1 remainder 5 |
| 7 | 14 ÷ 5 = 2 remainder 4 |
| 8 | 5 ÷ 4 = 1 remainder 1 |
| 9 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 140 and 56 | 280 |
| 131 and 109 | 14279 |
| 161 and 197 | 31717 |
| 173 and 58 | 10034 |
| 91 and 125 | 11375 |