Least Common Multiple (LCM) of 105 and 75
The least common multiple (LCM) of 105 and 75 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 75?
First, calculate the GCD of 105 and 75 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 105 ÷ 75 = 1 remainder 30 |
| 2 | 75 ÷ 30 = 2 remainder 15 |
| 3 | 30 ÷ 15 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 28 and 44 | 308 |
| 123 and 166 | 20418 |
| 45 and 184 | 8280 |
| 21 and 45 | 315 |
| 72 and 122 | 4392 |