Least Common Multiple (LCM) of 25 and 138
The least common multiple (LCM) of 25 and 138 is 3450.
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 25 and 138?
First, calculate the GCD of 25 and 138 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 25 ÷ 138 = 0 remainder 25 |
| 2 | 138 ÷ 25 = 5 remainder 13 |
| 3 | 25 ÷ 13 = 1 remainder 12 |
| 4 | 13 ÷ 12 = 1 remainder 1 |
| 5 | 12 ÷ 1 = 12 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 43 and 175 | 7525 |
| 97 and 187 | 18139 |
| 81 and 101 | 8181 |
| 22 and 44 | 44 |
| 113 and 140 | 15820 |