Least Common Multiple (LCM) of 125 and 170
The least common multiple (LCM) of 125 and 170 is 4250.
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 170?
First, calculate the GCD of 125 and 170 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 125 ÷ 170 = 0 remainder 125 |
| 2 | 170 ÷ 125 = 1 remainder 45 |
| 3 | 125 ÷ 45 = 2 remainder 35 |
| 4 | 45 ÷ 35 = 1 remainder 10 |
| 5 | 35 ÷ 10 = 3 remainder 5 |
| 6 | 10 ÷ 5 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 99 and 90 | 990 |
| 11 and 147 | 1617 |
| 164 and 46 | 3772 |
| 65 and 26 | 130 |
| 116 and 135 | 15660 |