Least Common Multiple (LCM) of 59 and 159
The least common multiple (LCM) of 59 and 159 is 9381.
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 59 and 159?
First, calculate the GCD of 59 and 159 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 59 ÷ 159 = 0 remainder 59 |
| 2 | 159 ÷ 59 = 2 remainder 41 |
| 3 | 59 ÷ 41 = 1 remainder 18 |
| 4 | 41 ÷ 18 = 2 remainder 5 |
| 5 | 18 ÷ 5 = 3 remainder 3 |
| 6 | 5 ÷ 3 = 1 remainder 2 |
| 7 | 3 ÷ 2 = 1 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 135 and 78 | 3510 |
| 168 and 170 | 14280 |
| 180 and 75 | 900 |
| 132 and 154 | 924 |
| 98 and 65 | 6370 |