Least Common Multiple (LCM) of 37 and 109
The least common multiple (LCM) of 37 and 109 is 4033.
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 37 and 109?
First, calculate the GCD of 37 and 109 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 37 ÷ 109 = 0 remainder 37 |
| 2 | 109 ÷ 37 = 2 remainder 35 |
| 3 | 37 ÷ 35 = 1 remainder 2 |
| 4 | 35 ÷ 2 = 17 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 109 and 85 | 9265 |
| 78 and 121 | 9438 |
| 77 and 146 | 11242 |
| 133 and 96 | 12768 |
| 133 and 94 | 12502 |