Least Common Multiple (LCM) of 102 and 64
The least common multiple (LCM) of 102 and 64 is 3264.
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 102 and 64?
First, calculate the GCD of 102 and 64 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 102 ÷ 64 = 1 remainder 38 |
| 2 | 64 ÷ 38 = 1 remainder 26 |
| 3 | 38 ÷ 26 = 1 remainder 12 |
| 4 | 26 ÷ 12 = 2 remainder 2 |
| 5 | 12 ÷ 2 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 13 and 81 | 1053 |
| 107 and 145 | 15515 |
| 200 and 155 | 6200 |
| 70 and 36 | 1260 |
| 35 and 105 | 105 |