Least Common Multiple (LCM) of 164 and 99
The least common multiple (LCM) of 164 and 99 is 16236.
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 99?
First, calculate the GCD of 164 and 99 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 164 ÷ 99 = 1 remainder 65 |
| 2 | 99 ÷ 65 = 1 remainder 34 |
| 3 | 65 ÷ 34 = 1 remainder 31 |
| 4 | 34 ÷ 31 = 1 remainder 3 |
| 5 | 31 ÷ 3 = 10 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 189 and 15 | 945 |
| 36 and 27 | 108 |
| 163 and 153 | 24939 |
| 35 and 32 | 1120 |
| 165 and 44 | 660 |