Least Common Multiple (LCM) of 117 and 138
The least common multiple (LCM) of 117 and 138 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 117 and 138?
First, calculate the GCD of 117 and 138 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 117 ÷ 138 = 0 remainder 117 |
| 2 | 138 ÷ 117 = 1 remainder 21 |
| 3 | 117 ÷ 21 = 5 remainder 12 |
| 4 | 21 ÷ 12 = 1 remainder 9 |
| 5 | 12 ÷ 9 = 1 remainder 3 |
| 6 | 9 ÷ 3 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 126 and 123 | 5166 |
| 90 and 180 | 180 |
| 141 and 130 | 18330 |
| 117 and 42 | 1638 |
| 192 and 69 | 4416 |