Least Common Multiple (LCM) of 138 and 173
The least common multiple (LCM) of 138 and 173 is 23874.
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 173?
First, calculate the GCD of 138 and 173 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 138 ÷ 173 = 0 remainder 138 |
| 2 | 173 ÷ 138 = 1 remainder 35 |
| 3 | 138 ÷ 35 = 3 remainder 33 |
| 4 | 35 ÷ 33 = 1 remainder 2 |
| 5 | 33 ÷ 2 = 16 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 61 and 197 | 12017 |
| 75 and 115 | 1725 |
| 114 and 46 | 2622 |
| 81 and 178 | 14418 |
| 10 and 146 | 730 |