Least Common Multiple (LCM) of 170 and 83
The least common multiple (LCM) of 170 and 83 is 14110.
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 83?
First, calculate the GCD of 170 and 83 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 170 ÷ 83 = 2 remainder 4 |
| 2 | 83 ÷ 4 = 20 remainder 3 |
| 3 | 4 ÷ 3 = 1 remainder 1 |
| 4 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 24 and 130 | 1560 |
| 150 and 12 | 300 |
| 42 and 95 | 3990 |
| 65 and 135 | 1755 |
| 113 and 68 | 7684 |