Least Common Multiple (LCM) of 67 and 125
The least common multiple (LCM) of 67 and 125 is 8375.
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 67 and 125?
First, calculate the GCD of 67 and 125 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 67 ÷ 125 = 0 remainder 67 |
| 2 | 125 ÷ 67 = 1 remainder 58 |
| 3 | 67 ÷ 58 = 1 remainder 9 |
| 4 | 58 ÷ 9 = 6 remainder 4 |
| 5 | 9 ÷ 4 = 2 remainder 1 |
| 6 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 148 and 86 | 6364 |
| 197 and 95 | 18715 |
| 114 and 17 | 1938 |
| 112 and 16 | 112 |
| 132 and 160 | 5280 |