Least Common Multiple (LCM) of 75 and 90
The least common multiple (LCM) of 75 and 90 is 450.
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 90?
First, calculate the GCD of 75 and 90 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 75 ÷ 90 = 0 remainder 75 |
| 2 | 90 ÷ 75 = 1 remainder 15 |
| 3 | 75 ÷ 15 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 155 and 188 | 29140 |
| 182 and 192 | 17472 |
| 38 and 72 | 1368 |
| 66 and 107 | 7062 |
| 193 and 199 | 38407 |