Least Common Multiple (LCM) of 138 and 191
The least common multiple (LCM) of 138 and 191 is 26358.
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 138 and 191?
First, calculate the GCD of 138 and 191 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 138 ÷ 191 = 0 remainder 138 |
| 2 | 191 ÷ 138 = 1 remainder 53 |
| 3 | 138 ÷ 53 = 2 remainder 32 |
| 4 | 53 ÷ 32 = 1 remainder 21 |
| 5 | 32 ÷ 21 = 1 remainder 11 |
| 6 | 21 ÷ 11 = 1 remainder 10 |
| 7 | 11 ÷ 10 = 1 remainder 1 |
| 8 | 10 ÷ 1 = 10 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 102 and 137 | 13974 |
| 120 and 162 | 3240 |
| 17 and 148 | 2516 |
| 69 and 175 | 12075 |
| 156 and 55 | 8580 |