Least Common Multiple (LCM) of 189 and 78
The least common multiple (LCM) of 189 and 78 is 4914.
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 189 and 78?
First, calculate the GCD of 189 and 78 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 189 ÷ 78 = 2 remainder 33 |
| 2 | 78 ÷ 33 = 2 remainder 12 |
| 3 | 33 ÷ 12 = 2 remainder 9 |
| 4 | 12 ÷ 9 = 1 remainder 3 |
| 5 | 9 ÷ 3 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 144 and 122 | 8784 |
| 76 and 167 | 12692 |
| 106 and 66 | 3498 |
| 177 and 193 | 34161 |
| 73 and 83 | 6059 |