Least Common Multiple (LCM) of 85 and 154
The least common multiple (LCM) of 85 and 154 is 13090.
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 154?
First, calculate the GCD of 85 and 154 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 85 ÷ 154 = 0 remainder 85 |
| 2 | 154 ÷ 85 = 1 remainder 69 |
| 3 | 85 ÷ 69 = 1 remainder 16 |
| 4 | 69 ÷ 16 = 4 remainder 5 |
| 5 | 16 ÷ 5 = 3 remainder 1 |
| 6 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 105 and 60 | 420 |
| 168 and 114 | 3192 |
| 44 and 163 | 7172 |
| 141 and 32 | 4512 |
| 71 and 188 | 13348 |