Least Common Multiple (LCM) of 138 and 189
The least common multiple (LCM) of 138 and 189 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 138 and 189?
First, calculate the GCD of 138 and 189 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 138 ÷ 189 = 0 remainder 138 |
| 2 | 189 ÷ 138 = 1 remainder 51 |
| 3 | 138 ÷ 51 = 2 remainder 36 |
| 4 | 51 ÷ 36 = 1 remainder 15 |
| 5 | 36 ÷ 15 = 2 remainder 6 |
| 6 | 15 ÷ 6 = 2 remainder 3 |
| 7 | 6 ÷ 3 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 184 and 160 | 3680 |
| 129 and 152 | 19608 |
| 101 and 120 | 12120 |
| 68 and 75 | 5100 |
| 183 and 144 | 8784 |