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 |
|---|---|
| 77 and 139 | 10703 |
| 22 and 177 | 3894 |
| 146 and 103 | 15038 |
| 54 and 70 | 1890 |
| 45 and 42 | 630 |