Least Common Multiple (LCM) of 170 and 100
The least common multiple (LCM) of 170 and 100 is 1700.
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 100?
First, calculate the GCD of 170 and 100 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 170 ÷ 100 = 1 remainder 70 |
| 2 | 100 ÷ 70 = 1 remainder 30 |
| 3 | 70 ÷ 30 = 2 remainder 10 |
| 4 | 30 ÷ 10 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 152 and 185 | 28120 |
| 91 and 157 | 14287 |
| 61 and 45 | 2745 |
| 194 and 182 | 17654 |
| 80 and 171 | 13680 |