Least Common Multiple (LCM) of 170 and 59
The least common multiple (LCM) of 170 and 59 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 170 and 59?
First, calculate the GCD of 170 and 59 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 170 ÷ 59 = 2 remainder 52 |
| 2 | 59 ÷ 52 = 1 remainder 7 |
| 3 | 52 ÷ 7 = 7 remainder 3 |
| 4 | 7 ÷ 3 = 2 remainder 1 |
| 5 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 159 and 125 | 19875 |
| 114 and 151 | 17214 |
| 169 and 18 | 3042 |
| 114 and 75 | 2850 |
| 107 and 77 | 8239 |