Least Common Multiple (LCM) of 110 and 75
The least common multiple (LCM) of 110 and 75 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 110 and 75?
First, calculate the GCD of 110 and 75 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 110 ÷ 75 = 1 remainder 35 |
| 2 | 75 ÷ 35 = 2 remainder 5 |
| 3 | 35 ÷ 5 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 89 and 178 | 178 |
| 96 and 33 | 1056 |
| 51 and 197 | 10047 |
| 101 and 174 | 17574 |
| 86 and 194 | 8342 |