Least Common Multiple (LCM) of 91 and 138
The least common multiple (LCM) of 91 and 138 is 12558.
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 91 and 138?
First, calculate the GCD of 91 and 138 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 91 ÷ 138 = 0 remainder 91 |
| 2 | 138 ÷ 91 = 1 remainder 47 |
| 3 | 91 ÷ 47 = 1 remainder 44 |
| 4 | 47 ÷ 44 = 1 remainder 3 |
| 5 | 44 ÷ 3 = 14 remainder 2 |
| 6 | 3 ÷ 2 = 1 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 120 and 111 | 4440 |
| 166 and 166 | 166 |
| 137 and 150 | 20550 |
| 39 and 101 | 3939 |
| 115 and 39 | 4485 |