Least Common Multiple (LCM) of 106 and 64
The least common multiple (LCM) of 106 and 64 is 3392.
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 106 and 64?
First, calculate the GCD of 106 and 64 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 106 ÷ 64 = 1 remainder 42 |
| 2 | 64 ÷ 42 = 1 remainder 22 |
| 3 | 42 ÷ 22 = 1 remainder 20 |
| 4 | 22 ÷ 20 = 1 remainder 2 |
| 5 | 20 ÷ 2 = 10 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 193 and 99 | 19107 |
| 60 and 38 | 1140 |
| 181 and 192 | 34752 |
| 78 and 173 | 13494 |
| 36 and 21 | 252 |