Least Common Multiple (LCM) of 25 and 78
The least common multiple (LCM) of 25 and 78 is 1950.
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 78?
First, calculate the GCD of 25 and 78 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 25 ÷ 78 = 0 remainder 25 |
| 2 | 78 ÷ 25 = 3 remainder 3 |
| 3 | 25 ÷ 3 = 8 remainder 1 |
| 4 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 106 and 37 | 3922 |
| 117 and 86 | 10062 |
| 47 and 19 | 893 |
| 160 and 80 | 160 |
| 50 and 172 | 4300 |