Least Common Multiple (LCM) of 164 and 59
The least common multiple (LCM) of 164 and 59 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 164 and 59?
First, calculate the GCD of 164 and 59 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 164 ÷ 59 = 2 remainder 46 |
| 2 | 59 ÷ 46 = 1 remainder 13 |
| 3 | 46 ÷ 13 = 3 remainder 7 |
| 4 | 13 ÷ 7 = 1 remainder 6 |
| 5 | 7 ÷ 6 = 1 remainder 1 |
| 6 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 132 and 156 | 1716 |
| 115 and 89 | 10235 |
| 160 and 96 | 480 |
| 157 and 95 | 14915 |
| 166 and 72 | 5976 |