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 |
|---|---|
| 133 and 71 | 9443 |
| 10 and 103 | 1030 |
| 155 and 145 | 4495 |
| 181 and 184 | 33304 |
| 197 and 167 | 32899 |