Least Common Multiple (LCM) of 37 and 178
The least common multiple (LCM) of 37 and 178 is 6586.
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 178?
First, calculate the GCD of 37 and 178 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 37 ÷ 178 = 0 remainder 37 |
| 2 | 178 ÷ 37 = 4 remainder 30 |
| 3 | 37 ÷ 30 = 1 remainder 7 |
| 4 | 30 ÷ 7 = 4 remainder 2 |
| 5 | 7 ÷ 2 = 3 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 17 and 41 | 697 |
| 86 and 169 | 14534 |
| 123 and 176 | 21648 |
| 103 and 23 | 2369 |
| 149 and 149 | 149 |