Least Common Multiple (LCM) of 37 and 112
The least common multiple (LCM) of 37 and 112 is 4144.
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 112?
First, calculate the GCD of 37 and 112 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 37 ÷ 112 = 0 remainder 37 |
| 2 | 112 ÷ 37 = 3 remainder 1 |
| 3 | 37 ÷ 1 = 37 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 112 and 14 | 112 |
| 118 and 68 | 4012 |
| 123 and 173 | 21279 |
| 110 and 178 | 9790 |
| 18 and 127 | 2286 |