Least Common Multiple (LCM) of 170 and 188
The least common multiple (LCM) of 170 and 188 is 15980.
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 188?
First, calculate the GCD of 170 and 188 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 170 ÷ 188 = 0 remainder 170 |
| 2 | 188 ÷ 170 = 1 remainder 18 |
| 3 | 170 ÷ 18 = 9 remainder 8 |
| 4 | 18 ÷ 8 = 2 remainder 2 |
| 5 | 8 ÷ 2 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 84 and 75 | 2100 |
| 138 and 175 | 24150 |
| 45 and 51 | 765 |
| 115 and 119 | 13685 |
| 46 and 62 | 1426 |