Least Common Multiple (LCM) of 37 and 192
The least common multiple (LCM) of 37 and 192 is 7104.
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 192?
First, calculate the GCD of 37 and 192 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 37 ÷ 192 = 0 remainder 37 |
| 2 | 192 ÷ 37 = 5 remainder 7 |
| 3 | 37 ÷ 7 = 5 remainder 2 |
| 4 | 7 ÷ 2 = 3 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 141 and 14 | 1974 |
| 135 and 94 | 12690 |
| 169 and 109 | 18421 |
| 112 and 180 | 5040 |
| 47 and 190 | 8930 |