Least Common Multiple (LCM) of 117 and 140
The least common multiple (LCM) of 117 and 140 is 16380.
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 140?
First, calculate the GCD of 117 and 140 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 117 ÷ 140 = 0 remainder 117 |
| 2 | 140 ÷ 117 = 1 remainder 23 |
| 3 | 117 ÷ 23 = 5 remainder 2 |
| 4 | 23 ÷ 2 = 11 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 45 and 76 | 3420 |
| 38 and 177 | 6726 |
| 173 and 38 | 6574 |
| 20 and 180 | 180 |
| 192 and 35 | 6720 |