Least Common Multiple (LCM) of 140 and 117
The least common multiple (LCM) of 140 and 117 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 140 and 117?
First, calculate the GCD of 140 and 117 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 140 ÷ 117 = 1 remainder 23 |
| 2 | 117 ÷ 23 = 5 remainder 2 |
| 3 | 23 ÷ 2 = 11 remainder 1 |
| 4 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 19 and 103 | 1957 |
| 103 and 81 | 8343 |
| 28 and 134 | 1876 |
| 176 and 162 | 14256 |
| 66 and 75 | 1650 |