Least Common Multiple (LCM) of 75 and 110
The least common multiple (LCM) of 75 and 110 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 110?
First, calculate the GCD of 75 and 110 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 75 ÷ 110 = 0 remainder 75 |
| 2 | 110 ÷ 75 = 1 remainder 35 |
| 3 | 75 ÷ 35 = 2 remainder 5 |
| 4 | 35 ÷ 5 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 133 and 112 | 2128 |
| 166 and 64 | 5312 |
| 197 and 85 | 16745 |
| 104 and 36 | 936 |
| 102 and 98 | 4998 |