Least Common Multiple (LCM) of 116 and 164
The least common multiple (LCM) of 116 and 164 is 4756.
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 164?
First, calculate the GCD of 116 and 164 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 116 ÷ 164 = 0 remainder 116 |
| 2 | 164 ÷ 116 = 1 remainder 48 |
| 3 | 116 ÷ 48 = 2 remainder 20 |
| 4 | 48 ÷ 20 = 2 remainder 8 |
| 5 | 20 ÷ 8 = 2 remainder 4 |
| 6 | 8 ÷ 4 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 108 and 22 | 1188 |
| 21 and 117 | 819 |
| 109 and 160 | 17440 |
| 61 and 23 | 1403 |
| 46 and 185 | 8510 |