Least Common Multiple (LCM) of 72 and 190
The least common multiple (LCM) of 72 and 190 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 72 and 190?
First, calculate the GCD of 72 and 190 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 72 ÷ 190 = 0 remainder 72 |
| 2 | 190 ÷ 72 = 2 remainder 46 |
| 3 | 72 ÷ 46 = 1 remainder 26 |
| 4 | 46 ÷ 26 = 1 remainder 20 |
| 5 | 26 ÷ 20 = 1 remainder 6 |
| 6 | 20 ÷ 6 = 3 remainder 2 |
| 7 | 6 ÷ 2 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 105 and 51 | 1785 |
| 48 and 68 | 816 |
| 170 and 89 | 15130 |
| 35 and 187 | 6545 |
| 77 and 73 | 5621 |