Least Common Multiple (LCM) of 114 and 37
The least common multiple (LCM) of 114 and 37 is 4218.
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 114 and 37?
First, calculate the GCD of 114 and 37 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 114 ÷ 37 = 3 remainder 3 |
| 2 | 37 ÷ 3 = 12 remainder 1 |
| 3 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 19 and 36 | 684 |
| 28 and 24 | 168 |
| 60 and 96 | 480 |
| 45 and 40 | 360 |
| 100 and 139 | 13900 |