Least Common Multiple (LCM) of 138 and 125
The least common multiple (LCM) of 138 and 125 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 138 and 125?
First, calculate the GCD of 138 and 125 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 138 ÷ 125 = 1 remainder 13 |
| 2 | 125 ÷ 13 = 9 remainder 8 |
| 3 | 13 ÷ 8 = 1 remainder 5 |
| 4 | 8 ÷ 5 = 1 remainder 3 |
| 5 | 5 ÷ 3 = 1 remainder 2 |
| 6 | 3 ÷ 2 = 1 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 110 and 90 | 990 |
| 106 and 29 | 3074 |
| 111 and 52 | 5772 |
| 85 and 62 | 5270 |
| 158 and 149 | 23542 |