Least Common Multiple (LCM) of 138 and 73
The least common multiple (LCM) of 138 and 73 is 10074.
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 73?
First, calculate the GCD of 138 and 73 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 138 ÷ 73 = 1 remainder 65 |
| 2 | 73 ÷ 65 = 1 remainder 8 |
| 3 | 65 ÷ 8 = 8 remainder 1 |
| 4 | 8 ÷ 1 = 8 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 53 and 200 | 10600 |
| 57 and 145 | 8265 |
| 45 and 89 | 4005 |
| 193 and 173 | 33389 |
| 123 and 40 | 4920 |