Least Common Multiple (LCM) of 34 and 25
The least common multiple (LCM) of 34 and 25 is 850.
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 25?
First, calculate the GCD of 34 and 25 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 34 ÷ 25 = 1 remainder 9 |
| 2 | 25 ÷ 9 = 2 remainder 7 |
| 3 | 9 ÷ 7 = 1 remainder 2 |
| 4 | 7 ÷ 2 = 3 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 57 and 12 | 228 |
| 103 and 197 | 20291 |
| 134 and 170 | 11390 |
| 100 and 112 | 2800 |
| 176 and 47 | 8272 |