Least Common Multiple (LCM) of 164 and 114
The least common multiple (LCM) of 164 and 114 is 9348.
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 164 and 114?
First, calculate the GCD of 164 and 114 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 164 ÷ 114 = 1 remainder 50 |
| 2 | 114 ÷ 50 = 2 remainder 14 |
| 3 | 50 ÷ 14 = 3 remainder 8 |
| 4 | 14 ÷ 8 = 1 remainder 6 |
| 5 | 8 ÷ 6 = 1 remainder 2 |
| 6 | 6 ÷ 2 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 150 and 61 | 9150 |
| 52 and 195 | 780 |
| 14 and 20 | 140 |
| 48 and 55 | 2640 |
| 114 and 113 | 12882 |