Least Common Multiple (LCM) of 102 and 172
The least common multiple (LCM) of 102 and 172 is 8772.
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 172?
First, calculate the GCD of 102 and 172 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 102 ÷ 172 = 0 remainder 102 |
| 2 | 172 ÷ 102 = 1 remainder 70 |
| 3 | 102 ÷ 70 = 1 remainder 32 |
| 4 | 70 ÷ 32 = 2 remainder 6 |
| 5 | 32 ÷ 6 = 5 remainder 2 |
| 6 | 6 ÷ 2 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 13 and 149 | 1937 |
| 107 and 135 | 14445 |
| 164 and 41 | 164 |
| 78 and 151 | 11778 |
| 20 and 135 | 540 |