Least Common Multiple (LCM) of 102 and 71
The least common multiple (LCM) of 102 and 71 is 7242.
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 71?
First, calculate the GCD of 102 and 71 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 102 ÷ 71 = 1 remainder 31 |
| 2 | 71 ÷ 31 = 2 remainder 9 |
| 3 | 31 ÷ 9 = 3 remainder 4 |
| 4 | 9 ÷ 4 = 2 remainder 1 |
| 5 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 10 and 28 | 140 |
| 165 and 113 | 18645 |
| 30 and 15 | 30 |
| 83 and 114 | 9462 |
| 142 and 117 | 16614 |