Least Common Multiple (LCM) of 105 and 25
The least common multiple (LCM) of 105 and 25 is 525.
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 105 and 25?
First, calculate the GCD of 105 and 25 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 105 ÷ 25 = 4 remainder 5 |
| 2 | 25 ÷ 5 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 149 and 72 | 10728 |
| 10 and 54 | 270 |
| 187 and 118 | 22066 |
| 57 and 100 | 5700 |
| 178 and 56 | 4984 |