Least Common Multiple (LCM) of 34 and 125
The least common multiple (LCM) of 34 and 125 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 34 and 125?
First, calculate the GCD of 34 and 125 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 34 ÷ 125 = 0 remainder 34 |
| 2 | 125 ÷ 34 = 3 remainder 23 |
| 3 | 34 ÷ 23 = 1 remainder 11 |
| 4 | 23 ÷ 11 = 2 remainder 1 |
| 5 | 11 ÷ 1 = 11 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 173 and 160 | 27680 |
| 115 and 179 | 20585 |
| 97 and 54 | 5238 |
| 28 and 182 | 364 |
| 158 and 11 | 1738 |