Least Common Multiple (LCM) of 189 and 138
The least common multiple (LCM) of 189 and 138 is 8694.
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 138?
First, calculate the GCD of 189 and 138 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 189 ÷ 138 = 1 remainder 51 |
| 2 | 138 ÷ 51 = 2 remainder 36 |
| 3 | 51 ÷ 36 = 1 remainder 15 |
| 4 | 36 ÷ 15 = 2 remainder 6 |
| 5 | 15 ÷ 6 = 2 remainder 3 |
| 6 | 6 ÷ 3 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 90 and 69 | 2070 |
| 109 and 94 | 10246 |
| 153 and 155 | 23715 |
| 67 and 34 | 2278 |
| 108 and 48 | 432 |