Least Common Multiple (LCM) of 37 and 172
The least common multiple (LCM) of 37 and 172 is 6364.
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 172?
First, calculate the GCD of 37 and 172 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 37 ÷ 172 = 0 remainder 37 |
| 2 | 172 ÷ 37 = 4 remainder 24 |
| 3 | 37 ÷ 24 = 1 remainder 13 |
| 4 | 24 ÷ 13 = 1 remainder 11 |
| 5 | 13 ÷ 11 = 1 remainder 2 |
| 6 | 11 ÷ 2 = 5 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 101 and 160 | 16160 |
| 54 and 179 | 9666 |
| 197 and 133 | 26201 |
| 159 and 84 | 4452 |
| 115 and 58 | 6670 |