Least Common Multiple (LCM) of 37 and 85
The least common multiple (LCM) of 37 and 85 is 3145.
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 85?
First, calculate the GCD of 37 and 85 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 37 ÷ 85 = 0 remainder 37 |
| 2 | 85 ÷ 37 = 2 remainder 11 |
| 3 | 37 ÷ 11 = 3 remainder 4 |
| 4 | 11 ÷ 4 = 2 remainder 3 |
| 5 | 4 ÷ 3 = 1 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 65 and 53 | 3445 |
| 194 and 81 | 15714 |
| 60 and 13 | 780 |
| 105 and 111 | 3885 |
| 111 and 91 | 10101 |