Least Common Multiple (LCM) of 59 and 164
The least common multiple (LCM) of 59 and 164 is 9676.
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 59 and 164?
First, calculate the GCD of 59 and 164 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 59 ÷ 164 = 0 remainder 59 |
| 2 | 164 ÷ 59 = 2 remainder 46 |
| 3 | 59 ÷ 46 = 1 remainder 13 |
| 4 | 46 ÷ 13 = 3 remainder 7 |
| 5 | 13 ÷ 7 = 1 remainder 6 |
| 6 | 7 ÷ 6 = 1 remainder 1 |
| 7 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 110 and 108 | 5940 |
| 25 and 195 | 975 |
| 99 and 49 | 4851 |
| 118 and 70 | 4130 |
| 177 and 120 | 7080 |