Least Common Multiple (LCM) of 37 and 107
The least common multiple (LCM) of 37 and 107 is 3959.
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 107?
First, calculate the GCD of 37 and 107 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 37 ÷ 107 = 0 remainder 37 |
| 2 | 107 ÷ 37 = 2 remainder 33 |
| 3 | 37 ÷ 33 = 1 remainder 4 |
| 4 | 33 ÷ 4 = 8 remainder 1 |
| 5 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 199 and 23 | 4577 |
| 65 and 158 | 10270 |
| 50 and 130 | 650 |
| 121 and 56 | 6776 |
| 167 and 10 | 1670 |