Least Common Multiple (LCM) of 105 and 159
The least common multiple (LCM) of 105 and 159 is 5565.
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 105 and 159?
First, calculate the GCD of 105 and 159 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 105 ÷ 159 = 0 remainder 105 |
| 2 | 159 ÷ 105 = 1 remainder 54 |
| 3 | 105 ÷ 54 = 1 remainder 51 |
| 4 | 54 ÷ 51 = 1 remainder 3 |
| 5 | 51 ÷ 3 = 17 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 40 and 72 | 360 |
| 157 and 145 | 22765 |
| 163 and 85 | 13855 |
| 39 and 177 | 2301 |
| 128 and 88 | 1408 |