Least Common Multiple (LCM) of 164 and 85
The least common multiple (LCM) of 164 and 85 is 13940.
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 85?
First, calculate the GCD of 164 and 85 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 164 ÷ 85 = 1 remainder 79 |
| 2 | 85 ÷ 79 = 1 remainder 6 |
| 3 | 79 ÷ 6 = 13 remainder 1 |
| 4 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 113 and 37 | 4181 |
| 153 and 187 | 1683 |
| 11 and 79 | 869 |
| 63 and 74 | 4662 |
| 115 and 167 | 19205 |