Least Common Multiple (LCM) of 109 and 75
The least common multiple (LCM) of 109 and 75 is 8175.
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 109 and 75?
First, calculate the GCD of 109 and 75 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 109 ÷ 75 = 1 remainder 34 |
| 2 | 75 ÷ 34 = 2 remainder 7 |
| 3 | 34 ÷ 7 = 4 remainder 6 |
| 4 | 7 ÷ 6 = 1 remainder 1 |
| 5 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 117 and 37 | 4329 |
| 37 and 196 | 7252 |
| 43 and 193 | 8299 |
| 148 and 21 | 3108 |
| 118 and 180 | 10620 |