Least Common Multiple (LCM) of 108 and 37
The least common multiple (LCM) of 108 and 37 is 3996.
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 108 and 37?
First, calculate the GCD of 108 and 37 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 108 ÷ 37 = 2 remainder 34 |
| 2 | 37 ÷ 34 = 1 remainder 3 |
| 3 | 34 ÷ 3 = 11 remainder 1 |
| 4 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 42 and 39 | 546 |
| 135 and 169 | 22815 |
| 32 and 65 | 2080 |
| 100 and 165 | 3300 |
| 142 and 42 | 2982 |