Least Common Multiple (LCM) of 15 and 75
The least common multiple (LCM) of 15 and 75 is 75.
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 15 and 75?
First, calculate the GCD of 15 and 75 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 15 ÷ 75 = 0 remainder 15 |
| 2 | 75 ÷ 15 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 177 and 58 | 10266 |
| 31 and 71 | 2201 |
| 123 and 76 | 9348 |
| 98 and 177 | 17346 |
| 160 and 36 | 1440 |