Least Common Multiple (LCM) of 159 and 85
The least common multiple (LCM) of 159 and 85 is 13515.
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 159 and 85?
First, calculate the GCD of 159 and 85 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 159 ÷ 85 = 1 remainder 74 |
| 2 | 85 ÷ 74 = 1 remainder 11 |
| 3 | 74 ÷ 11 = 6 remainder 8 |
| 4 | 11 ÷ 8 = 1 remainder 3 |
| 5 | 8 ÷ 3 = 2 remainder 2 |
| 6 | 3 ÷ 2 = 1 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 29 and 105 | 3045 |
| 12 and 11 | 132 |
| 147 and 145 | 21315 |
| 85 and 47 | 3995 |
| 115 and 28 | 3220 |