Least Common Multiple (LCM) of 138 and 91
The least common multiple (LCM) of 138 and 91 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 138 and 91?
First, calculate the GCD of 138 and 91 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 138 ÷ 91 = 1 remainder 47 |
| 2 | 91 ÷ 47 = 1 remainder 44 |
| 3 | 47 ÷ 44 = 1 remainder 3 |
| 4 | 44 ÷ 3 = 14 remainder 2 |
| 5 | 3 ÷ 2 = 1 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 188 and 179 | 33652 |
| 38 and 41 | 1558 |
| 144 and 114 | 2736 |
| 14 and 105 | 210 |
| 34 and 184 | 3128 |