Least Common Multiple (LCM) of 37 and 113
The least common multiple (LCM) of 37 and 113 is 4181.
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 113?
First, calculate the GCD of 37 and 113 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 37 ÷ 113 = 0 remainder 37 |
| 2 | 113 ÷ 37 = 3 remainder 2 |
| 3 | 37 ÷ 2 = 18 remainder 1 |
| 4 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 127 and 10 | 1270 |
| 82 and 178 | 7298 |
| 170 and 89 | 15130 |
| 71 and 177 | 12567 |
| 168 and 105 | 840 |