Least Common Multiple (LCM) of 102 and 67
The least common multiple (LCM) of 102 and 67 is 6834.
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 67?
First, calculate the GCD of 102 and 67 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 102 ÷ 67 = 1 remainder 35 |
| 2 | 67 ÷ 35 = 1 remainder 32 |
| 3 | 35 ÷ 32 = 1 remainder 3 |
| 4 | 32 ÷ 3 = 10 remainder 2 |
| 5 | 3 ÷ 2 = 1 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 89 and 193 | 17177 |
| 11 and 56 | 616 |
| 129 and 53 | 6837 |
| 58 and 123 | 7134 |
| 171 and 13 | 2223 |