Least Common Multiple (LCM) of 102 and 73
The least common multiple (LCM) of 102 and 73 is 7446.
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 73?
First, calculate the GCD of 102 and 73 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 102 ÷ 73 = 1 remainder 29 |
| 2 | 73 ÷ 29 = 2 remainder 15 |
| 3 | 29 ÷ 15 = 1 remainder 14 |
| 4 | 15 ÷ 14 = 1 remainder 1 |
| 5 | 14 ÷ 1 = 14 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 99 and 111 | 3663 |
| 85 and 171 | 14535 |
| 150 and 177 | 8850 |
| 84 and 80 | 1680 |
| 103 and 45 | 4635 |