Least Common Multiple (LCM) of 116 and 158
The least common multiple (LCM) of 116 and 158 is 9164.
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 116 and 158?
First, calculate the GCD of 116 and 158 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 116 ÷ 158 = 0 remainder 116 |
| 2 | 158 ÷ 116 = 1 remainder 42 |
| 3 | 116 ÷ 42 = 2 remainder 32 |
| 4 | 42 ÷ 32 = 1 remainder 10 |
| 5 | 32 ÷ 10 = 3 remainder 2 |
| 6 | 10 ÷ 2 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 100 and 195 | 3900 |
| 42 and 19 | 798 |
| 118 and 140 | 8260 |
| 145 and 93 | 13485 |
| 178 and 50 | 4450 |