Least Common Multiple (LCM) of 125 and 138
The least common multiple (LCM) of 125 and 138 is 17250.
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 125 and 138?
First, calculate the GCD of 125 and 138 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 125 ÷ 138 = 0 remainder 125 |
| 2 | 138 ÷ 125 = 1 remainder 13 |
| 3 | 125 ÷ 13 = 9 remainder 8 |
| 4 | 13 ÷ 8 = 1 remainder 5 |
| 5 | 8 ÷ 5 = 1 remainder 3 |
| 6 | 5 ÷ 3 = 1 remainder 2 |
| 7 | 3 ÷ 2 = 1 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 114 and 160 | 9120 |
| 87 and 191 | 16617 |
| 178 and 73 | 12994 |
| 172 and 133 | 22876 |
| 105 and 126 | 630 |