Least Common Multiple (LCM) of 37 and 176
The least common multiple (LCM) of 37 and 176 is 6512.
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 176?
First, calculate the GCD of 37 and 176 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 37 ÷ 176 = 0 remainder 37 |
| 2 | 176 ÷ 37 = 4 remainder 28 |
| 3 | 37 ÷ 28 = 1 remainder 9 |
| 4 | 28 ÷ 9 = 3 remainder 1 |
| 5 | 9 ÷ 1 = 9 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 43 and 129 | 129 |
| 114 and 55 | 6270 |
| 57 and 40 | 2280 |
| 78 and 30 | 390 |
| 147 and 20 | 2940 |