Least Common Multiple (LCM) of 138 and 117
The least common multiple (LCM) of 138 and 117 is 5382.
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 117?
First, calculate the GCD of 138 and 117 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 138 ÷ 117 = 1 remainder 21 |
| 2 | 117 ÷ 21 = 5 remainder 12 |
| 3 | 21 ÷ 12 = 1 remainder 9 |
| 4 | 12 ÷ 9 = 1 remainder 3 |
| 5 | 9 ÷ 3 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 126 and 91 | 1638 |
| 99 and 154 | 1386 |
| 145 and 88 | 12760 |
| 76 and 101 | 7676 |
| 21 and 185 | 3885 |