Least Common Multiple (LCM) of 36 and 190
The least common multiple (LCM) of 36 and 190 is 3420.
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 36 and 190?
First, calculate the GCD of 36 and 190 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 36 ÷ 190 = 0 remainder 36 |
| 2 | 190 ÷ 36 = 5 remainder 10 |
| 3 | 36 ÷ 10 = 3 remainder 6 |
| 4 | 10 ÷ 6 = 1 remainder 4 |
| 5 | 6 ÷ 4 = 1 remainder 2 |
| 6 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 48 and 106 | 2544 |
| 110 and 181 | 19910 |
| 114 and 21 | 798 |
| 198 and 162 | 1782 |
| 72 and 175 | 12600 |