Least Common Multiple (LCM) of 37 and 71
The least common multiple (LCM) of 37 and 71 is 2627.
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 71?
First, calculate the GCD of 37 and 71 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 37 ÷ 71 = 0 remainder 37 |
| 2 | 71 ÷ 37 = 1 remainder 34 |
| 3 | 37 ÷ 34 = 1 remainder 3 |
| 4 | 34 ÷ 3 = 11 remainder 1 |
| 5 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 135 and 31 | 4185 |
| 112 and 192 | 1344 |
| 153 and 106 | 16218 |
| 197 and 28 | 5516 |
| 149 and 38 | 5662 |