Least Common Multiple (LCM) of 102 and 117
The least common multiple (LCM) of 102 and 117 is 3978.
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 117?
First, calculate the GCD of 102 and 117 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 102 ÷ 117 = 0 remainder 102 |
| 2 | 117 ÷ 102 = 1 remainder 15 |
| 3 | 102 ÷ 15 = 6 remainder 12 |
| 4 | 15 ÷ 12 = 1 remainder 3 |
| 5 | 12 ÷ 3 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 47 and 106 | 4982 |
| 64 and 115 | 7360 |
| 45 and 31 | 1395 |
| 53 and 71 | 3763 |
| 73 and 156 | 11388 |