Least Common Multiple (LCM) of 25 and 69
The least common multiple (LCM) of 25 and 69 is 1725.
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 25 and 69?
First, calculate the GCD of 25 and 69 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 25 ÷ 69 = 0 remainder 25 |
| 2 | 69 ÷ 25 = 2 remainder 19 |
| 3 | 25 ÷ 19 = 1 remainder 6 |
| 4 | 19 ÷ 6 = 3 remainder 1 |
| 5 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 143 and 69 | 9867 |
| 172 and 37 | 6364 |
| 45 and 144 | 720 |
| 47 and 160 | 7520 |
| 108 and 198 | 1188 |