Least Common Multiple (LCM) of 45 and 25
The least common multiple (LCM) of 45 and 25 is 225.
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 45 and 25?
First, calculate the GCD of 45 and 25 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 45 ÷ 25 = 1 remainder 20 |
| 2 | 25 ÷ 20 = 1 remainder 5 |
| 3 | 20 ÷ 5 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 32 and 55 | 1760 |
| 31 and 136 | 4216 |
| 105 and 187 | 19635 |
| 138 and 188 | 12972 |
| 95 and 20 | 380 |