Least Common Multiple (LCM) of 25 and 48
The least common multiple (LCM) of 25 and 48 is 1200.
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 48?
First, calculate the GCD of 25 and 48 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 25 ÷ 48 = 0 remainder 25 |
| 2 | 48 ÷ 25 = 1 remainder 23 |
| 3 | 25 ÷ 23 = 1 remainder 2 |
| 4 | 23 ÷ 2 = 11 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 166 and 172 | 14276 |
| 155 and 165 | 5115 |
| 107 and 126 | 13482 |
| 173 and 91 | 15743 |
| 57 and 121 | 6897 |