Least Common Multiple (LCM) of 190 and 138
The least common multiple (LCM) of 190 and 138 is 13110.
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 138?
First, calculate the GCD of 190 and 138 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 190 ÷ 138 = 1 remainder 52 |
| 2 | 138 ÷ 52 = 2 remainder 34 |
| 3 | 52 ÷ 34 = 1 remainder 18 |
| 4 | 34 ÷ 18 = 1 remainder 16 |
| 5 | 18 ÷ 16 = 1 remainder 2 |
| 6 | 16 ÷ 2 = 8 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 20 and 25 | 100 |
| 97 and 71 | 6887 |
| 105 and 120 | 840 |
| 170 and 148 | 12580 |
| 161 and 77 | 1771 |