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 |
|---|---|
| 160 and 30 | 480 |
| 130 and 14 | 910 |
| 194 and 138 | 13386 |
| 192 and 28 | 1344 |
| 150 and 42 | 1050 |