Least Common Multiple (LCM) of 190 and 72
The least common multiple (LCM) of 190 and 72 is 6840.
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 190 and 72?
First, calculate the GCD of 190 and 72 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 190 ÷ 72 = 2 remainder 46 |
| 2 | 72 ÷ 46 = 1 remainder 26 |
| 3 | 46 ÷ 26 = 1 remainder 20 |
| 4 | 26 ÷ 20 = 1 remainder 6 |
| 5 | 20 ÷ 6 = 3 remainder 2 |
| 6 | 6 ÷ 2 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 74 and 87 | 6438 |
| 90 and 125 | 2250 |
| 168 and 66 | 1848 |
| 45 and 96 | 1440 |
| 173 and 116 | 20068 |