Least Common Multiple (LCM) of 164 and 51
The least common multiple (LCM) of 164 and 51 is 8364.
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 51?
First, calculate the GCD of 164 and 51 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 164 ÷ 51 = 3 remainder 11 |
| 2 | 51 ÷ 11 = 4 remainder 7 |
| 3 | 11 ÷ 7 = 1 remainder 4 |
| 4 | 7 ÷ 4 = 1 remainder 3 |
| 5 | 4 ÷ 3 = 1 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 197 and 141 | 27777 |
| 123 and 87 | 3567 |
| 154 and 89 | 13706 |
| 185 and 36 | 6660 |
| 15 and 164 | 2460 |