Least Common Multiple (LCM) of 75 and 22
The least common multiple (LCM) of 75 and 22 is 1650.
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 75 and 22?
First, calculate the GCD of 75 and 22 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 75 ÷ 22 = 3 remainder 9 |
| 2 | 22 ÷ 9 = 2 remainder 4 |
| 3 | 9 ÷ 4 = 2 remainder 1 |
| 4 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 120 and 188 | 5640 |
| 21 and 120 | 840 |
| 150 and 28 | 2100 |
| 25 and 144 | 3600 |
| 195 and 119 | 23205 |