Least Common Multiple (LCM) of 37 and 131
The least common multiple (LCM) of 37 and 131 is 4847.
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 131?
First, calculate the GCD of 37 and 131 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 37 ÷ 131 = 0 remainder 37 |
| 2 | 131 ÷ 37 = 3 remainder 20 |
| 3 | 37 ÷ 20 = 1 remainder 17 |
| 4 | 20 ÷ 17 = 1 remainder 3 |
| 5 | 17 ÷ 3 = 5 remainder 2 |
| 6 | 3 ÷ 2 = 1 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 42 and 104 | 2184 |
| 109 and 185 | 20165 |
| 50 and 136 | 3400 |
| 101 and 118 | 11918 |
| 117 and 181 | 21177 |