Least Common Multiple (LCM) of 164 and 169
The least common multiple (LCM) of 164 and 169 is 27716.
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 169?
First, calculate the GCD of 164 and 169 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 164 ÷ 169 = 0 remainder 164 |
| 2 | 169 ÷ 164 = 1 remainder 5 |
| 3 | 164 ÷ 5 = 32 remainder 4 |
| 4 | 5 ÷ 4 = 1 remainder 1 |
| 5 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 140 and 15 | 420 |
| 18 and 71 | 1278 |
| 111 and 11 | 1221 |
| 30 and 68 | 1020 |
| 71 and 92 | 6532 |