Least Common Multiple (LCM) of 117 and 142
The least common multiple (LCM) of 117 and 142 is 16614.
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 142?
First, calculate the GCD of 117 and 142 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 117 ÷ 142 = 0 remainder 117 |
| 2 | 142 ÷ 117 = 1 remainder 25 |
| 3 | 117 ÷ 25 = 4 remainder 17 |
| 4 | 25 ÷ 17 = 1 remainder 8 |
| 5 | 17 ÷ 8 = 2 remainder 1 |
| 6 | 8 ÷ 1 = 8 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 71 and 100 | 7100 |
| 103 and 121 | 12463 |
| 24 and 32 | 96 |
| 35 and 188 | 6580 |
| 85 and 87 | 7395 |