Least Common Multiple (LCM) of 109 and 36
The least common multiple (LCM) of 109 and 36 is 3924.
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 36?
First, calculate the GCD of 109 and 36 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 109 ÷ 36 = 3 remainder 1 |
| 2 | 36 ÷ 1 = 36 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 44 and 55 | 220 |
| 144 and 71 | 10224 |
| 64 and 184 | 1472 |
| 67 and 52 | 3484 |
| 82 and 75 | 6150 |