Least Common Multiple (LCM) of 59 and 170
The least common multiple (LCM) of 59 and 170 is 10030.
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 170?
First, calculate the GCD of 59 and 170 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 59 ÷ 170 = 0 remainder 59 |
| 2 | 170 ÷ 59 = 2 remainder 52 |
| 3 | 59 ÷ 52 = 1 remainder 7 |
| 4 | 52 ÷ 7 = 7 remainder 3 |
| 5 | 7 ÷ 3 = 2 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 73 and 20 | 1460 |
| 59 and 92 | 5428 |
| 121 and 12 | 1452 |
| 196 and 83 | 16268 |
| 54 and 140 | 3780 |