Least Common Multiple (LCM) of 25 and 165
The least common multiple (LCM) of 25 and 165 is 825.
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 165?
First, calculate the GCD of 25 and 165 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 25 ÷ 165 = 0 remainder 25 |
| 2 | 165 ÷ 25 = 6 remainder 15 |
| 3 | 25 ÷ 15 = 1 remainder 10 |
| 4 | 15 ÷ 10 = 1 remainder 5 |
| 5 | 10 ÷ 5 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 113 and 50 | 5650 |
| 135 and 120 | 1080 |
| 41 and 72 | 2952 |
| 186 and 56 | 5208 |
| 110 and 31 | 3410 |