Least Common Multiple (LCM) of 138 and 85
The least common multiple (LCM) of 138 and 85 is 11730.
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 85?
First, calculate the GCD of 138 and 85 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 138 ÷ 85 = 1 remainder 53 |
| 2 | 85 ÷ 53 = 1 remainder 32 |
| 3 | 53 ÷ 32 = 1 remainder 21 |
| 4 | 32 ÷ 21 = 1 remainder 11 |
| 5 | 21 ÷ 11 = 1 remainder 10 |
| 6 | 11 ÷ 10 = 1 remainder 1 |
| 7 | 10 ÷ 1 = 10 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 130 and 180 | 2340 |
| 66 and 148 | 4884 |
| 89 and 34 | 3026 |
| 178 and 38 | 3382 |
| 57 and 20 | 1140 |