Least Common Multiple (LCM) of 99 and 159
The least common multiple (LCM) of 99 and 159 is 5247.
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 99 and 159?
First, calculate the GCD of 99 and 159 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 99 ÷ 159 = 0 remainder 99 |
| 2 | 159 ÷ 99 = 1 remainder 60 |
| 3 | 99 ÷ 60 = 1 remainder 39 |
| 4 | 60 ÷ 39 = 1 remainder 21 |
| 5 | 39 ÷ 21 = 1 remainder 18 |
| 6 | 21 ÷ 18 = 1 remainder 3 |
| 7 | 18 ÷ 3 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 82 and 169 | 13858 |
| 17 and 185 | 3145 |
| 123 and 71 | 8733 |
| 17 and 152 | 2584 |
| 67 and 46 | 3082 |