Least Common Multiple (LCM) of 168 and 189
The least common multiple (LCM) of 168 and 189 is 1512.
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 168 and 189?
First, calculate the GCD of 168 and 189 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 168 ÷ 189 = 0 remainder 168 |
| 2 | 189 ÷ 168 = 1 remainder 21 |
| 3 | 168 ÷ 21 = 8 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 102 and 196 | 9996 |
| 55 and 26 | 1430 |
| 14 and 86 | 602 |
| 67 and 89 | 5963 |
| 190 and 39 | 7410 |