Least Common Multiple (LCM) of 25 and 72
The least common multiple (LCM) of 25 and 72 is 1800.
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 72?
First, calculate the GCD of 25 and 72 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 25 ÷ 72 = 0 remainder 25 |
| 2 | 72 ÷ 25 = 2 remainder 22 |
| 3 | 25 ÷ 22 = 1 remainder 3 |
| 4 | 22 ÷ 3 = 7 remainder 1 |
| 5 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 182 and 35 | 910 |
| 26 and 26 | 26 |
| 173 and 52 | 8996 |
| 128 and 106 | 6784 |
| 77 and 39 | 3003 |