Least Common Multiple (LCM) of 178 and 189
The least common multiple (LCM) of 178 and 189 is 33642.
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 178 and 189?
First, calculate the GCD of 178 and 189 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 178 ÷ 189 = 0 remainder 178 |
| 2 | 189 ÷ 178 = 1 remainder 11 |
| 3 | 178 ÷ 11 = 16 remainder 2 |
| 4 | 11 ÷ 2 = 5 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 102 and 199 | 20298 |
| 114 and 90 | 1710 |
| 130 and 113 | 14690 |
| 44 and 164 | 1804 |
| 32 and 84 | 672 |